diff --git a/lbmpy_tests/full_scenarios/phasefield_allen_cahn/phasefield-capillary-wave.ipynb b/lbmpy_tests/full_scenarios/phasefield_allen_cahn/phasefield-capillary-wave.ipynb
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index 0000000000000000000000000000000000000000..e8339d83477a4f7b2a953d945bcb89c24b0700e7
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@@ -0,0 +1,1131 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import os\n",
+ "\n",
+ "import time\n",
+ "from tqdm.notebook import tqdm\n",
+ "\n",
+ "import numpy as np\n",
+ "import math\n",
+ "from scipy.special import erfc\n",
+ "\n",
+ "from pystencils.session import *\n",
+ "from lbmpy.session import *\n",
+ "\n",
+ "from pystencils.simp import sympy_cse\n",
+ "from pystencils.boundaries import BoundaryHandling\n",
+ "\n",
+ "from lbmpy.phasefield_allen_cahn.parameter_calculation import AllenCahnParameters\n",
+ "from lbmpy.phasefield_allen_cahn.contact_angle import ContactAngle\n",
+ "from lbmpy.phasefield_allen_cahn.kernel_equations import *\n",
+ "\n",
+ "from lbmpy.advanced_streaming import LBMPeriodicityHandling\n",
+ "from lbmpy.boundaries import NoSlip, LatticeBoltzmannBoundaryHandling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If `pycuda` is installed the simulation automatically runs on GPU"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "No pycuda installed\n"
+ ]
+ }
+ ],
+ "source": [
+ "try:\n",
+ " import pycuda\n",
+ "except ImportError:\n",
+ " pycuda = None\n",
+ " gpu = False\n",
+ " target = ps.Target.CPU\n",
+ " print('No pycuda installed')\n",
+ "\n",
+ "if pycuda:\n",
+ " gpu = True\n",
+ " target = ps.Target.GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Capillary wave simulated with a phase-field model for immiscible fluids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Geometry Setup\n",
+ "\n",
+ "First of all the stencils for the phase-field LB step as well as the stencil for the hydrodynamic LB step are defined. According to the stencils the simulation runs either in 2D or 3D"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "stencil_phase = LBStencil(Stencil.D2Q9)\n",
+ "stencil_hydro = LBStencil(Stencil.D2Q9)\n",
+ "assert(stencil_hydro.D == stencil_phase.D)\n",
+ "\n",
+ "dimensions = stencil_phase.D"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "timesteps = 238800\n",
+ "Re = 10\n",
+ "Pe = 0.41876046901171776\n",
+ "Cn = 0.1\n",
+ "domain_width = 50\n",
+ "fluid_depth = 25.0\n",
+ "amplitude = 0.5\n",
+ "relaxation_rate_heavy = 1.99\n",
+ "mobility = 0.02\n",
+ "interface_width = 5\n",
+ "density_heavy = 1.0\n",
+ "density_light = 0.001\n",
+ "density_ratio = 1000\n",
+ "kinematic_viscosity_heavy = 0.0008375209380234356\n",
+ "kinematic_viscosity_light = 0.0008375209380234356\n",
+ "kinematic_viscosity_ratio = 1\n",
+ "dynamic_viscosity_heavy = 0.0008375209380234356\n",
+ "dynamic_viscosity_light = 8.375209380234357e-07\n",
+ "dynamic_viscosity_ratio = 1000.0\n",
+ "wavelength = 50\n",
+ "wavenumber = 0.12566370614359174\n",
+ "wave_frequency = 0.00033500837520937423\n",
+ "surface_tension = 5.6612953740701554e-05\n",
+ "gravitational_acceleration = 0\n"
+ ]
+ }
+ ],
+ "source": [
+ "# user defined input\n",
+ "\n",
+ "Re = 10 # Reynolds number\n",
+ "domain_width = 50\n",
+ "fluid_depth = 0.5 * domain_width\n",
+ "amplitude = 0.01 * domain_width\n",
+ "relaxation_rate_heavy = 1.99\n",
+ "mobility = 0.02 # phase field mobility\n",
+ "interface_width = 5 # phase field interface width\n",
+ "density_heavy = 1.0 # density of heavy phase\n",
+ "density_ratio = 1000\n",
+ "density_light = density_heavy / density_ratio # density of light phase\n",
+ "kinematic_viscosity_ratio = 1\n",
+ "\n",
+ "kinematic_viscosity_heavy = 1 / 3 * (1 / relaxation_rate_heavy - 0.5)\n",
+ "kinematic_viscosity_light = kinematic_viscosity_heavy / kinematic_viscosity_ratio\n",
+ "wavelength = domain_width\n",
+ "wavenumber = 2.0 * np.pi / domain_width\n",
+ "wave_frequency = Re * kinematic_viscosity_heavy / domain_width / amplitude # angular wave frequency\n",
+ "surface_tension = wave_frequency**2 * (density_heavy + density_light) / wavenumber**3\n",
+ "gravitational_acceleration = 0\n",
+ "Pe = domain_width * amplitude * wave_frequency / mobility # Peclet number\n",
+ "Cn = interface_width / domain_width # Cahn number\n",
+ "dynamic_viscosity_heavy = kinematic_viscosity_heavy * density_heavy\n",
+ "relaxation_time_heavy = 3.0 * kinematic_viscosity_heavy\n",
+ "kinematic_viscosity_light = kinematic_viscosity_heavy / kinematic_viscosity_ratio\n",
+ "dynamic_viscosity_light = kinematic_viscosity_light * density_light\n",
+ "relaxation_time_light = 3.0 * kinematic_viscosity_light\n",
+ "\n",
+ "timesteps = int(80 / wave_frequency)\n",
+ "\n",
+ "data_extract_frequency = int(0.1 / wave_frequency)\n",
+ "vtk_output_frequency = int(1 / wave_frequency)\n",
+ "vtk_output_path = \"vtk_out/capillary-wave\"\n",
+ "vtk_base_directory = vtk_output_path.split(\"/\")[0] # create directory for vtk-output if it does not yet exist\n",
+ "if not os.path.exists(vtk_base_directory):\n",
+ " os.mkdir(os.getcwd() + \"/\" + vtk_base_directory)\n",
+ "\n",
+ "domain_size = (domain_width, domain_width)\n",
+ "filename = \"pf-re-\" + str(Re) + \"-resolution-\" + str(domain_width) + \".txt\"\n",
+ "\n",
+ "print(\"timesteps =\", timesteps)\n",
+ "print(\"Re =\", Re)\n",
+ "print(\"Pe =\", Pe)\n",
+ "print(\"Cn =\", Cn)\n",
+ "print(\"domain_width =\", domain_width)\n",
+ "print(\"fluid_depth =\", fluid_depth)\n",
+ "print(\"amplitude =\", amplitude)\n",
+ "print(\"relaxation_rate_heavy =\", relaxation_rate_heavy)\n",
+ "print(\"mobility =\", mobility)\n",
+ "print(\"interface_width =\", interface_width)\n",
+ "print(\"density_heavy =\", density_heavy)\n",
+ "print(\"density_light =\", density_light)\n",
+ "print(\"density_ratio =\", density_ratio)\n",
+ "print(\"kinematic_viscosity_heavy =\", kinematic_viscosity_heavy)\n",
+ "print(\"kinematic_viscosity_light =\", kinematic_viscosity_light)\n",
+ "print(\"kinematic_viscosity_ratio =\", kinematic_viscosity_ratio)\n",
+ "print(\"dynamic_viscosity_heavy =\", dynamic_viscosity_heavy)\n",
+ "print(\"dynamic_viscosity_light =\", dynamic_viscosity_light)\n",
+ "print(\"dynamic_viscosity_ratio =\", dynamic_viscosity_heavy/dynamic_viscosity_light)\n",
+ "print(\"wavelength =\", wavelength)\n",
+ "print(\"wavenumber =\", wavenumber)\n",
+ "print(\"wave_frequency =\", wave_frequency)\n",
+ "print(\"surface_tension =\", surface_tension)\n",
+ "print(\"gravitational_acceleration =\", gravitational_acceleration)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "parameters = AllenCahnParameters(density_heavy=density_heavy, density_light=density_light,\n",
+ " dynamic_viscosity_heavy=dynamic_viscosity_heavy,\n",
+ " dynamic_viscosity_light=dynamic_viscosity_light,\n",
+ " surface_tension=surface_tension, mobility=mobility,\n",
+ " interface_thickness=interface_width)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <table style=\"border:none; width: 100%\">\n",
+ " <tr style=\"border:none\">\n",
+ " <th style=\"border:none\" >Name</th>\n",
+ " <th style=\"border:none\" >SymPy Symbol </th>\n",
+ " <th style=\"border:none\" >Value</th>\n",
+ " </tr>\n",
+ " <tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Density heavy phase</td>\n",
+ " <td style=\"border:none\">$\\rho_{H}$</td>\n",
+ " <td style=\"border:none\">$1.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Density light phase</td>\n",
+ " <td style=\"border:none\">$\\rho_{L}$</td>\n",
+ " <td style=\"border:none\">$0.001$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation time heavy phase</td>\n",
+ " <td style=\"border:none\">$\\tau_{H}$</td>\n",
+ " <td style=\"border:none\">$0.00251256281407031$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation time light phase</td>\n",
+ " <td style=\"border:none\">$\\tau_{L}$</td>\n",
+ " <td style=\"border:none\">$0.00251256281407031$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation rate Allen Cahn LB</td>\n",
+ " <td style=\"border:none\">$\\omega_{\\phi}$</td>\n",
+ " <td style=\"border:none\">$1.78571428571429$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Gravitational acceleration</td>\n",
+ " <td style=\"border:none\">$F_{g}$</td>\n",
+ " <td style=\"border:none\">$0.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Interface thickness</td>\n",
+ " <td style=\"border:none\">$W$</td>\n",
+ " <td style=\"border:none\">$5$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Mobility</td>\n",
+ " <td style=\"border:none\">$M_{m}$</td>\n",
+ " <td style=\"border:none\">$0.02$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Surface tension</td>\n",
+ " <td style=\"border:none\">$\\sigma$</td>\n",
+ " <td style=\"border:none\">$5.66129537407016 \\cdot 10^{-5}$</td>\n",
+ " </tr>\n",
+ "\n",
+ " </table>\n",
+ " "
+ ],
+ "text/plain": [
+ "<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x146131580>"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "parameters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fields\n",
+ "\n",
+ "As a next step all fields which are needed get defined. To do so we create a `datahandling` object. More details about it can be found in the third tutorial of the [pystencils framework]( http://pycodegen.pages.walberla.net/pystencils/). Basically it holds all fields and manages the kernel runs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create a datahandling object\n",
+ "dh = ps.create_data_handling((domain_size), periodicity=(True, False), parallel=False, default_target=target)\n",
+ "\n",
+ "# fields \n",
+ "g = dh.add_array(\"g\", values_per_cell=len(stencil_hydro))\n",
+ "dh.fill(\"g\", 0.0, ghost_layers=True)\n",
+ "h = dh.add_array(\"h\",values_per_cell=len(stencil_phase))\n",
+ "dh.fill(\"h\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "g_tmp = dh.add_array(\"g_tmp\", values_per_cell=len(stencil_hydro))\n",
+ "dh.fill(\"g_tmp\", 0.0, ghost_layers=True)\n",
+ "h_tmp = dh.add_array(\"h_tmp\",values_per_cell=len(stencil_phase))\n",
+ "dh.fill(\"h_tmp\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "u = dh.add_array(\"u\", values_per_cell=dh.dim)\n",
+ "dh.fill(\"u\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "rho = dh.add_array(\"rho\", values_per_cell=1)\n",
+ "dh.fill(\"rho\", 1.0, ghost_layers=True)\n",
+ "\n",
+ "C = dh.add_array(\"C\")\n",
+ "dh.fill(\"C\", 0.0, ghost_layers=True)\n",
+ "C_tmp = dh.add_array(\"C_tmp\")\n",
+ "dh.fill(\"C_tmp\", 0.0, ghost_layers=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# set the frequency of the file outputs\n",
+ "vtk_writer = dh.create_vtk_writer(vtk_output_path, [\"C\", \"u\", \"rho\"], ghost_layers=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rho_L = parameters.symbolic_density_light\n",
+ "rho_H = parameters.symbolic_density_heavy\n",
+ "density = rho_L + C.center * (rho_H - rho_L)\n",
+ "\n",
+ "body_force = [0, 0, 0]\n",
+ "body_force[1] = parameters.symbolic_gravitational_acceleration * density"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Definition of the lattice Boltzmann methods"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "w_c = parameters.symbolic_omega_phi\n",
+ "\n",
+ "config_phase = LBMConfig(stencil=stencil_phase, method=Method.MRT, compressible=True,\n",
+ " delta_equilibrium=False,\n",
+ " force=sp.symbols(\"F_:2\"), velocity_input=u,\n",
+ " weighted=True, relaxation_rates=[0, w_c, w_c, 1, 1, 1, 1, 1, 1],\n",
+ " output={'density': C_tmp}, kernel_type='stream_pull_collide')\n",
+ "\n",
+ "method_phase = create_lb_method(lbm_config=config_phase)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "omega = parameters.omega(C)\n",
+ "config_hydro = LBMConfig(stencil=stencil_hydro, method=Method.MRT, compressible=False,\n",
+ " weighted=True, relaxation_rates=[omega, 1, 1, 1],\n",
+ " force=sp.symbols(\"F_:2\"),\n",
+ " output={'velocity': u}, kernel_type='collide_stream_push')\n",
+ "\n",
+ "method_hydro = create_lb_method(lbm_config=config_hydro)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Initialization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n",
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "h_updates = initializer_kernel_phase_field_lb(method_phase, C, u, h, parameters)\n",
+ "g_updates = initializer_kernel_hydro_lb(method_hydro, 1, u, g)\n",
+ "\n",
+ "h_init = ps.create_kernel(h_updates, target=dh.default_target, cpu_openmp=True).compile()\n",
+ "g_init = ps.create_kernel(g_updates, target=dh.default_target, cpu_openmp=True).compile()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# initialize the phase field\n",
+ "def initialize_phasefield():\n",
+ " Nx = domain_size[0]\n",
+ " Ny = domain_size[1]\n",
+ " \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False):\n",
+ " # get x as cell center coordinate, i.e., including shift with 0.5\n",
+ " x = np.zeros_like(block.midpoint_arrays[0])\n",
+ " x[:, :] = block.midpoint_arrays[0]\n",
+ " \n",
+ " # get y as cell center coordinate, i.e., including shift with 0.5\n",
+ " y = np.zeros_like(block.midpoint_arrays[1])\n",
+ " y[:, :] = block.midpoint_arrays[1] \n",
+ " \n",
+ " tmp = fluid_depth + amplitude * np.cos(x / (Nx - 1) * np.pi * 2 + np.pi)\n",
+ " \n",
+ " # initialize diffuse interface with tanh profile\n",
+ " init_values = 0.5 - 0.5 * np.tanh((y - tmp) / (interface_width / 2))\n",
+ " \n",
+ " block[\"C\"][:, :] = init_values\n",
+ " block[\"C_tmp\"][:, :] = init_values\n",
+ " \n",
+ " if gpu:\n",
+ " dh.all_to_gpu() \n",
+ " \n",
+ " dh.run_kernel(h_init, **parameters.symbolic_to_numeric_map)\n",
+ " dh.run_kernel(g_init)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot initial profile\n",
+ "x = np.arange(0, domain_size[0], 1) # start,stop,step\n",
+ "y = fluid_depth + amplitude * np.cos(x / (domain_size[0] - 1) * np.pi * 2 + np.pi)\n",
+ "\n",
+ "plt.plot(x,y, marker='o')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "asymmetric: 25.111260466978155 25.11126046697816\n"
+ ]
+ }
+ ],
+ "source": [
+ "# check symmetry of sine-curve\n",
+ "for i in range(0, domain_size[0] - 1):\n",
+ " if (i >= domain_size[0] * 0.5):\n",
+ " continue\n",
+ " if (y[i] != y[domain_size[0] - 1 - i]):\n",
+ " print(\"asymmetric:\", y[i], y[domain_size[0] - 1 - i])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "initialize_phasefield()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scalar_field(dh.cpu_arrays[\"C\"])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot initial interface profile\n",
+ "x = np.arange(0, domain_size[1]+2, 1) # start,stop,step\n",
+ "y = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), :]\n",
+ "\n",
+ "plt.plot(x,y, marker='o')\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "force_h = interface_tracking_force(C, stencil_phase, parameters)\n",
+ "hydro_force = hydrodynamic_force(g, C, method_hydro, parameters, body_force)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Definition of the LB update rules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "lbm_optimisation = LBMOptimisation(symbolic_field=h, symbolic_temporary_field=h_tmp)\n",
+ "allen_cahn_update_rule = create_lb_update_rule(lbm_config=config_phase,\n",
+ " lbm_optimisation=lbm_optimisation)\n",
+ "\n",
+ "allen_cahn_update_rule = add_interface_tracking_force(allen_cahn_update_rule, force_h)\n",
+ "\n",
+ "ast_kernel = ps.create_kernel(allen_cahn_update_rule, target=dh.default_target, cpu_openmp=True)\n",
+ "kernel_allen_cahn_lb = ast_kernel.compile()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "force_Assignments = hydrodynamic_force_assignments(g, u, C, method_hydro, parameters, body_force)\n",
+ "\n",
+ "lbm_optimisation = LBMOptimisation(symbolic_field=g, symbolic_temporary_field=g_tmp)\n",
+ "hydro_lb_update_rule = create_lb_update_rule(lbm_config=config_hydro,\n",
+ " lbm_optimisation=lbm_optimisation)\n",
+ "\n",
+ "hydro_lb_update_rule = add_hydrodynamic_force(hydro_lb_update_rule, force_Assignments, C, g, parameters)\n",
+ "\n",
+ "ast_kernel = ps.create_kernel(hydro_lb_update_rule, target=dh.default_target, cpu_openmp=True)\n",
+ "kernel_hydro_lb = ast_kernel.compile()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Boundary Conditions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# periodic Boundarys for g, h and C\n",
+ "periodic_BC_C = dh.synchronization_function(C.name, target=dh.default_target, optimization = {\"openmp\": True})\n",
+ "\n",
+ "periodic_BC_g = LBMPeriodicityHandling(stencil=stencil_hydro, data_handling=dh, pdf_field_name=g.name,\n",
+ " streaming_pattern='push')\n",
+ "periodic_BC_h = LBMPeriodicityHandling(stencil=stencil_phase, data_handling=dh, pdf_field_name=h.name,\n",
+ " streaming_pattern='pull')\n",
+ "\n",
+ "# No slip boundary for the phasefield lbm\n",
+ "bh_allen_cahn = LatticeBoltzmannBoundaryHandling(method_phase, dh, 'h',\n",
+ " target=dh.default_target, name='boundary_handling_h',\n",
+ " streaming_pattern='pull')\n",
+ "\n",
+ "# No slip boundary for the velocityfield lbm\n",
+ "bh_hydro = LatticeBoltzmannBoundaryHandling(method_hydro, dh, 'g' ,\n",
+ " target=dh.default_target, name='boundary_handling_g',\n",
+ " streaming_pattern='push')\n",
+ "\n",
+ "contact_angle = BoundaryHandling(dh, C.name, stencil_hydro, target=dh.default_target)\n",
+ "contact = ContactAngle(90, interface_width)\n",
+ "\n",
+ "wall = NoSlip()\n",
+ "if dimensions == 2:\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, 0])\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, -1])\n",
+ "\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, 0])\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, -1])\n",
+ " \n",
+ " contact_angle.set_boundary(contact, make_slice[:, 0])\n",
+ " contact_angle.set_boundary(contact, make_slice[:, -1])\n",
+ "else:\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, 0, :])\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, -1, :])\n",
+ "\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, 0, :])\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, -1, :])\n",
+ " \n",
+ " contact_angle.set_boundary(contact, make_slice[:, 0, :])\n",
+ " contact_angle.set_boundary(contact, make_slice[:, -1, :])\n",
+ "\n",
+ "\n",
+ "bh_allen_cahn.prepare()\n",
+ "bh_hydro.prepare()\n",
+ "contact_angle.prepare()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Full timestep"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# definition of the timestep for the immiscible fluids model\n",
+ "def timeloop():\n",
+ " # Solve the interface tracking LB step with boundary conditions\n",
+ " periodic_BC_h()\n",
+ " bh_allen_cahn() \n",
+ " dh.run_kernel(kernel_allen_cahn_lb, **parameters.symbolic_to_numeric_map)\n",
+ " dh.swap(\"C\", \"C_tmp\")\n",
+ " \n",
+ " # apply the three phase-phase contact angle\n",
+ " contact_angle()\n",
+ " # periodic BC of the phase-field\n",
+ " periodic_BC_C()\n",
+ " \n",
+ " # solve the hydro LB step with boundary conditions\n",
+ " dh.run_kernel(kernel_hydro_lb, **parameters.symbolic_to_numeric_map)\n",
+ " periodic_BC_g()\n",
+ " bh_hydro()\n",
+ " \n",
+ " # compute density (only for vtk output)\n",
+ " # must be done BEFORE swapping fields to avoid having outdated values\n",
+ " compute_density()\n",
+ " \n",
+ " # field swaps\n",
+ " dh.swap(\"h\", \"h_tmp\")\n",
+ " dh.swap(\"g\", \"g_tmp\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def initialize_hydrostatic_pressure(): \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False): \n",
+ " \n",
+ " # get y as cell center coordinate, i.e., including shift with 0.5\n",
+ " y = np.zeros_like(block.midpoint_arrays[1])\n",
+ " y[:, :] = block.midpoint_arrays[1]\n",
+ " \n",
+ " # compute hydrostatic density\n",
+ " rho_hydrostatic = 1 + 3 * gravitational_acceleration * (y - fluid_depth)\n",
+ " \n",
+ " # subtract 1 because PDFs in incompressible LBM are centered around zero in lbmpy\n",
+ " rho_hydrostatic -= 1\n",
+ "\n",
+ " # set equilibrium PDFs with velocity=0 and rho; \n",
+ " for i in range(0, stencil_hydro.Q, 1):\n",
+ " block[\"g\"][:,:,i] = method_hydro.weights[i] * rho_hydrostatic[:,:]\n",
+ " block[\"g_tmp\"][:,:,i] = method_hydro.weights[i] * rho_hydrostatic[:,:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def compute_density(): \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False):\n",
+ " # PDFs in incompressible LBM are centered around zero in lbmpy\n",
+ " # => add 1 to whole sum, i.e., initialize with 1\n",
+ " block[\"rho\"].fill(1);\n",
+ " \n",
+ " # compute density\n",
+ " for i in range(block[\"g\"].shape[-1]):\n",
+ " block[\"rho\"][:,:] += block[\"g\"][:,:,i]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "if (gravitational_acceleration != 0):\n",
+ " initialize_hydrostatic_pressure()\n",
+ " compute_density()\n",
+ " plt.scalar_field(dh.cpu_arrays[\"rho\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "================================= start of the simulation ===================================\n"
+ ]
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "1227a4e61d374ab0b4630ee22b5b35a8",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ " 0%| | 0/238800 [00:00<?, ?it/s]"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "\n",
+ "time needed for the calculation: 92.7764 seconds\n",
+ "MLUPS: 6.43\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"================================= start of the simulation ===================================\")\n",
+ "\n",
+ "start = time.time()\n",
+ "\n",
+ "pbar = tqdm(total=timesteps)\n",
+ "\n",
+ "timestep = []\n",
+ "surface_position = []\n",
+ "symmetry_norm = []\n",
+ "\n",
+ "for i in range(0, timesteps):\n",
+ " \n",
+ " sum_c_2 = 0.0\n",
+ " sum_delta_c_2 = 0.0\n",
+ " \n",
+ " # write vtk output\n",
+ " if(i % vtk_output_frequency == 0):\n",
+ " if gpu:\n",
+ " dh.to_cpu(\"C\")\n",
+ " dh.to_cpu(\"u\")\n",
+ " dh.to_cpu(\"rho\")\n",
+ " vtk_writer(i)\n",
+ " \n",
+ " # extract data (to be written to file)\n",
+ " if(i % data_extract_frequency == 0):\n",
+ " if gpu:\n",
+ " dh.to_cpu(\"C\")\n",
+ " dh.to_cpu(\"u\")\n",
+ " dh.to_cpu(\"rho\")\n",
+ " \n",
+ " pbar.update(data_extract_frequency)\n",
+ " \n",
+ " timestep.append(i)\n",
+ " \n",
+ " ny = domain_size[1]\n",
+ "\n",
+ " # get index containing phase field value < 0.5\n",
+ " i1 = np.argmax(dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), :] < 0.5)\n",
+ " i0 = i1 - 1 # index containing phase field value >= 0.5 \n",
+ "\n",
+ " f0 = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), i0] # phase field value >= 0.5\n",
+ " f1 = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), i1] # phase field value < 0.5\n",
+ "\n",
+ " # coordinate of cell center is index+0.5-1 (0.5 to get to cell center; -1 to remove ghost layer from index)\n",
+ " y0 = i0 + 0.5 - 1\n",
+ " y1 = i1 + 0.5 - 1\n",
+ "\n",
+ " #interpolate\n",
+ " surface_position.append( y0 + (y1 - y0) / (f1 - f0) * (0.5 - f0) )\n",
+ " \n",
+ " # evaluate symmetry in x-direction\n",
+ " for y in range(0, domain_size[1] - 1):\n",
+ " for x in range(0, domain_size[0] - 1):\n",
+ " if (x >= domain_size[0] * 0.5):\n",
+ " continue\n",
+ " \n",
+ " x_mirrored = domain_size[0] - 1 - x;\n",
+ " sum_c_2 += dh.cpu_arrays[\"C\"][x, y]**2\n",
+ " sum_delta_c_2 += (dh.cpu_arrays[\"C\"][x, y] - dh.cpu_arrays[\"C\"][x_mirrored, y])**2\n",
+ " \n",
+ " symmetry_norm.append( (sum_delta_c_2 / sum_c_2)**2 )\n",
+ " \n",
+ " timeloop()\n",
+ "\n",
+ "pbar.close()\n",
+ "end = time.time()\n",
+ "sim_time = end - start\n",
+ "print(\"\\n\")\n",
+ "print(\"time needed for the calculation: %4.4f\" % sim_time , \"seconds\")\n",
+ "\n",
+ "nrOfCells = np.prod(domain_size)\n",
+ "mlups = nrOfCells * timesteps / sim_time * 1e-6\n",
+ "\n",
+ "print(\"MLUPS: %4.2f\" % mlups)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.image.AxesImage at 0x146e329a0>"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "if gpu:\n",
+ " dh.to_cpu(\"C\")\n",
+ " dh.to_cpu(\"u\")\n",
+ " dh.to_cpu(\"rho\")\n",
+ "\n",
+ "plt.scalar_field(dh.cpu_arrays[\"C\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# non-dimensionalize time and surface position\n",
+ "t_nd = [value * wave_frequency for value in timestep]\n",
+ "a_nd = [(value - fluid_depth) / amplitude for value in surface_position]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot surface position over time\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$a/-$', fontsize=18)\n",
+ "plt.grid(color='black', linestyle='-', linewidth=0.1)\n",
+ "plt.plot(t_nd, a_nd, color=(0.121, 0.231, 0.4))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot analytical solutions\n",
+ "\n",
+ "# analytical model from Prosperetti, Motion of two superposed viscous fluids, 1981, doi: 10.1063/1.863522\n",
+ "nu = kinematic_viscosity_heavy\n",
+ "k = wavenumber\n",
+ "omega_0 = wave_frequency\n",
+ "rho_u = density_heavy\n",
+ "rho_l = density_light\n",
+ "a0 = amplitude\n",
+ "beta = rho_l * rho_u / (rho_l + rho_u)**2\n",
+ "\n",
+ "k2nu = k**2 * nu # helper variable\n",
+ "\n",
+ "# polynomials from equation (21)\n",
+ "p0 = (1 - 4 * beta) * k2nu**2 + omega_0**2\n",
+ "p1 = 4 * (1 - 3 * beta) * k2nu**1.5\n",
+ "p2 = 2 * (1 - 6 * beta) * k2nu\n",
+ "p3 = -4 * beta * k2nu**(0.5)\n",
+ "p4 = 1\n",
+ "p = [p0, p1, p2, p3, p4]\n",
+ "\n",
+ "# get roots of equation (21)\n",
+ "z = np.polynomial.polynomial.polyroots(p)\n",
+ "\n",
+ "Z = np.array([(z[1] - z[0]) * (z[2] - z[0]) * (z[3] - z[0]),\n",
+ " (z[0] - z[1]) * (z[2] - z[1]) * (z[3] - z[1]),\n",
+ " (z[0] - z[2]) * (z[1] - z[2]) * (z[3] - z[2]),\n",
+ " (z[0] - z[3]) * (z[1] - z[3]) * (z[2] - z[3])])\n",
+ "\n",
+ "t = np.arange(0, timesteps, 1)\n",
+ "\n",
+ "# equation (20)\n",
+ "tmp0 = (1 - 4 * beta) * k2nu**2 # helper variable\n",
+ "term0 = 4 * tmp0 / (8 * tmp0 + omega_0**2) * a0 * erfc((k2nu * t)**0.5) # first term in equation (20)\n",
+ "\n",
+ "term1 = 0.0\n",
+ "for i in range(0, 4, 1):\n",
+ " tmp1 = z[i]**2 - k2nu # helper variable\n",
+ " term1 += z[i] / Z[i] * omega_0**2 * a0 / tmp1 * np.exp(tmp1 * t) * erfc(z[i] * t**0.5)\n",
+ "\n",
+ "a = np.real(term0 + term1)\n",
+ "\n",
+ "# non-dimesionalize time and surface position\n",
+ "pos_anal_lin_org = a / a0\n",
+ "t_anal_org = t * omega_0\n",
+ "\n",
+ "# non-dimesionalize time and surface position\n",
+ "a_anal_nd = a / amplitude\n",
+ "t_anal_nd = t * wave_frequency\n",
+ "\n",
+ "plt.plot(t_anal_nd, a_anal_nd, label=\"analytical solution\")\n",
+ "plt.plot(t_nd, a_nd, label=\"simulation\")\n",
+ "\n",
+ "# correction factor from Denner et al., Dispersion and viscous attenuation of capillary waves with finite amplitude, 2016, doi: 10.1140/epjst/e2016-60199-2\n",
+ "# model is now valid for initial amplitudes of about 0.1*wavelength\n",
+ "a0_hat = a0 / wavelength\n",
+ "C = -4.5 * a0_hat**3 + 5.3 * a0_hat**2 + 0.18 * a0_hat + 1\n",
+ "a_anal_nd_corr = a_anal_nd * C\n",
+ "t_anal_nd_corr = t_anal_nd * C\n",
+ "plt.plot(t_anal_nd_corr, a_anal_nd_corr, label=\"linear analytical solution with correction factor\")\n",
+ "\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$a/-$', fontsize=18)\n",
+ "plt.legend()\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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PRMSDwAnALyt8Vm4VWpoByvN2DbuSJEmSNFEHHXYjoplSuL0jpbQtpbQGWAP877hrZlEKvZW6ATg2IpaU73kR8Id7XPMQpTD904g4BDgeWDGBZ+VWobnUHC5SJUmSJEnVqWTO7gjwM+CN+7ogpbQlpfSDSotIKY0AbwC+DdwNXJZSujMiXhcRrytf9l7gKRFxO/B94O0ppfqalHsAv9mzK0mSJEmaqIPu2U0ppYhYBwwc8OIJSCldDVy9x7FPj/t+LfCcyXh2XhQK5Z7dXYZdSZIkSarGRPbZPW8yCtH4nt397qgkSZIkSTqASsPuvwHHR8RbJ6OYmc5hzJIkSZKUjUrD7j2U9r/9YET8OCJeFRFHTUJdM5JhV5IkSZKyUc0+u08vv1JE9FPeY5eJ7bMrHgu7Q8MOY5YkSZKkamS9z+4zmdg+uwIKLS5QJUmSJElZqLRnd7eM99kVDmOWJEmSpKxMKOxGRCtwBLAtpbR67HhKaQtQ8T67KikUDLuSJEmSlIVKF6giIv4R2AzcBayKiI0RcbELVVXPrYckSZIkKRsV9exGxF8CfwP8AvgREMBJwMuBl0bE76eUvpV1kTOFw5glSZIkKRuVDmP+M+CqlNLvjD8YEYuALwP/HRGnp5TuzqrAmaSlubxAlWFXkiRJkqpS6TDmxcBVex5MKT0MnAc8RKnnVxPQ2NhAU2ODYVeSJEmSqlRp2N0AzNrbiZTSTuDzlLYf0gQVWpoNu5IkSZJUpUrD7veAV5ZXY96bfmBOdSXNbIVCM7t2uUCVJEmSJFWj0rD7j8BC4JqIOGYv558PPFx1VTOYPbuSJEmSVL2KFqhKKT0QES8CvgHcExE/pLQF0RDwDOB04G2ZVzmDGHYlSZIkqXqVrsZMSuk7EfFE4F3AC4Bzy6f6gbenlD6SXXkzT6GlybArSZIkSVWqOOwCpJRWAq+KiFdTGtacUkqrsyxspiq0NDM07JxdSZIkSapGxWE3IhqBI4EdKaW1OEc3Uw5jliRJkqTqVRR2I+KpwNeB+eX3g8AtwM3jXveklFLGdc4YhZZmduwaqnUZkiRJklTXKu3Z/RjQCfwTsAs4idKiVL8FBJCAbUB3hjXOKIWWJvoGttW6DEmSJEmqa5WG3aXAB1JK7xl/MCJ6gNMoBd/TMqptRnIYsyRJkiRVr9Kwuw7YsOfBlFI/8MPyS1UoFAy7kiRJklSthgqvvww4exLqUFmpZ9fVmCVJkiSpGpWG3U8CT4iIl05GMYKWZvfZlSRJkqRqVRp2VwGHA/8ZEVdExB9GxFGTUNeM5ZxdSZIkSapepXN2PwqcAiwDLii/UkT0U9p26CbgppTSZVkWOZMUWko9uyklIqLW5UiSJElSXaoo7KaU3jr2fUQsBk4tv5aVvz6T0vZDht0JKrQ0UywmRkaLNDc11rocSZIkSapLlfbs7pZSegh4CLhi7FhEzKYUejVBhZZmAHYNDRt2JUmSJGmCKp2zu18ppc0ppe9nec+ZplAoh91dztuVJEmSpInKNOyqemM9u0PDbj8kSZIkSRNl2M2ZQktpZLkrMkuSJEnSxBl2c2b8nF1JkiRJ0sQYdnPGsCtJkiRJ1Ztw2I2I3og4KstiNC7s7nLOriRJkiRNVDU9u28G7s+qEJXYsytJkiRJ1XMYc84UCi5QJUmSJEnVMuzmTEuzPbuSJEmSVC3Dbs649ZAkSZIkVc+wmzOPzdl1gSpJkiRJmijDbs64QJUkSZIkVc+wmzOFwtjWQ4ZdSZIkSZqo3ITdiDgvIu6NiAci4h37uObsiLg1Iu6MiB9PdY1TwZ5dSZIkSapeU60LAIiIRuCTwLOB1cANEXFlSumucdf0Ap8CzkspPRQR82tS7CRramygoSEYGnbOriRJkiRNVF56dp8EPJBSWpFSGgIuBS7c45o/BC5PKT0EkFJaP8U1TomIoNDSbM+uJEmSJFWhmp7dKL+ysAB4eNz71cCT97jmOKA5In4EdAEfSyn95/5uWiwWGRwczKjE7O2rtpbmJga3bs917dOVv+f5ZLvkj22ST7ZL/tgm+WS75I9tkk/13i7V9Ox+FFiSUR17C81pj/dNwOnAbwPPBd4VEcc97kYRr4mIGyPixo0bN2ZU3tQqtDQ5jFmSJEmSqjDhnt2UUj/Qn1Edq4FF494vBNbu5ZqNKaVtwLaI+AlwCnDfHnVdDFwMsHz58tTV1ZVRiZNnzxpbCy0U0+OPa+r4e59Ptkv+2Cb5ZLvkj22ST7ZL/tgm+VSv7ZKXObs3AMdGxJKIaAEuAq7c45orgKdHRFNEtFMa5nz3FNc5JQotzW49JEmSJElVyMVqzCmlkYh4A/BtoBH4fErpzoh4Xfn8p1NKd0fENcCvgCLwuZTSHbWrevK4QJUkSZIkVScXYRcgpXQ1cPUexz69x/sPAR+ayrpqoaWliV1DztmVJEmSpImqaBhzRHw0IronqxiV2LMrSZIkSdWpdM7unwMPRMRrIyKrbYe0B8OuJEmSJFWn0rB7MnAj8O/ALRFxdtYFqbT1kGFXkiRJkiauorCbUro3pXQ+cAHQBnw/Ir4eEUdMSnUzVKln1zm7kiRJkjRRE9p6KKX0LeAJwNuBZwF3R8T7IqIjy+JmKocxS5IkSVJ1JrzPbkppJKX0YeBY4CuUgu99EfGyrIqbqQy7kiRJklSdCYfdcWYBPwKuBQ4DvhgR10fEGRnce0YqFJoYchizJEmSJE1YRfvsRsShwJPGvZYDPeXTCbgD+CVwNnBdRHwEeEdKKWVV8Exgz64kSZIkVaeisAuspRRqA9gM/By4HrgO+EVKaStARDQBfw28p3z9O7IqeCYotDQzPDLK6GiRxsYsOt8lSZIkaWY56LAbEc3AdyjNz70+pXTfvq5NKY0A74+IbuAVGHYrUmhpBmBoeIS2xpYaVyNJkiRJ9aeSbsMR4NnA4fsLunu4DTik4qpmuLGw61BmSZIkSZqYgw675Xm3jwADFdz/28AfVlrUTFdoKXW4G3YlSZIkaWIqnRB6OXDewV6cUtqSUrq0wmfMeC1jPbu7DLuSJEmSNBGVht1/A46PiLdORjEqsWdXkiRJkqpTadi9B1gAfDAifhwRr4qIoyahrhntsTm77rUrSZIkSRNR6dZDHwKWAacCTy+/UkT0AzcDNwE3pZQuy7LImcYFqiRJkiSpOhWF3ZTS28e+j4gFwGmUgu/Y65mU9tU17FbBsCtJkiRJ1ako7EbEu4EvppQeTCmtAdYA/zvu/CxKoVdVMOxKkiRJUnUqnbP7LuCsfZ0sr778g+pKkgtUSZIkSVJ1Kg27+xURfxgRD2Z5z5moUHCBKkmSJEmqxgGHMUfEG4FnAdeXD3Xs5/JGYHEGdc1oDmOWJEmSpOoczJzdQUpDly+gtPjUpyPivcAtlFZgHns9VL5u4+SUOnO49ZAkSZIkVeeAYTel9EXgixFxDHAfcBVQpLQS83PHLhv3kS9nXOOMY8+uJEmSJFXnoFdjTik9EBFXAJ9JKV0DEBFzgNMprcB8FLAC+PhkFDqTuECVJEmSJFWn0n12X7jH+03Ad8ovZaSl2bArSZIkSdWoKOyOiYhDgWOBPuCulNJolkXNdBFBoaWZXbsMu5IkSZI0ERVtPRQRrRFxCbAG+BFwK/CM8rnIuriZrKWlaUoWqBrYuoOPfPYKPviZ/5n0Z0mSJEnSVKl0n913AX8AfAh4BTA+4M6OiIcj4kUZ1TajFVqap2QY87987go+8aWr+dSXr2HVmg2T/jxJkiRJmgqVht3fBz6fUnoHcPX4E+X5u78AXpJRbTPaVIXd62+5n0WHzQXgJ7+8a9KfJ0mSJElTodKwuxC4YT/nf0VpSyJVqdDSNOlht39wO/euWMPvnX8WCw+bw08Nu5IkSZKmiUoXqHoEOHw/59cAh0y8HI0p9exO7pzdW+5cQUqJM04+hnUb+rjq+zdQLBZpaKj0ZyCSJEmSlC+VppprgFdGRGEf5+cBO6orSTA1w5hvvmMFjY0NLFu6hCcct4jBbTtZv6l/Up8pSZIkSVOh0rD7AaAXuApYMP5EOQC/DLg/k8pmuEJLM0OT3LP74MPrWXDIbNrbChyxYB4AK1e7SJUkSZKk+ldR2E0pPQScB5wM/BJIwMsi4r3ATcAJwKeyLnImmoo5u6vXbWThYXMAOHLBfAAeckVmSZIkSdNAxZMzU0q/AE4EPgmsA14O/C1wNPDhlNIlmVY4QxUKkz+MefW6TbtXYj5s/iyaGhtYuWb9pD5TkiRJkqZCpQtUAZBS2gy8FXhrRMwHeoDVKSXn62Zksufs7tw1xIZNAyw8tNSz29TUyMLD5rrXriRJkqRpYUJhd7yU0nrA7sCMTfZqzGse3QywexgzwBEL5jmMWZIkSdK0UPEw5oiYExHnRMTTy726mgST3bO7+pFNACw8dO7uY0csmMfKNRtIKU3acyVJkiRpKlTUsxsRFwKXAO3jjq0Fbh7/SimtybLImWiyF6jaHXbH9ewuPHQOg1t3sHX7Tro62ibt2ZIkSZI02SodxvzPwE5KC1INUFqo6jTgqcAF5WsS0JhVgTNVS/Mkh911m2huamT+nJ7dx+bPLX2/flO/YVeSJElSXas07C4C3pVS+vieJyLiCOB0YFkGdc14hUJpn92UEhGR+f3Xb+pn/pweGhsfG8k+FnzXb+zn6MWHZv5MSZIkSZoqlYbdu9nHPN+U0ipgFXB5tUWpNGcXYNfQCK2F5szvv3HzAHNnd//Gsd1hd1N/5s+TJEmSpKlU6QJVHwNeGhGZD1OOiPMi4t6IeCAi3rGf686IiNGI+L2sa8iTx8Lu5Axl3rB5gLmzun7j2Lxy2N1g2JUkSZJU5yoKuymlLwPXApdHxJwDXX+wyuH5k8DzgKXASyJi6T6u+2fg21k9O68mO+zurWe3u7ONQkuzPbuSJEmS6l6lqzEvABZTWoxqbUT8ELie0irMN1WxCvOTgAdSSivKz7kUuBC4a4/r3gh8AzjjYG5aLBYZHBycYEmTb3+1pWJpj93NW/poa6l4h6j9KhaLbNoySHdn6+NqmDu7izXrNuX6920yzdRfd97ZLvljm+ST7ZI/tkk+2S75Y5vkU723S6Vzdr8APAu4FdgCnAo8h9IKzETERkqh9/wK77sAeHjc+9XAk8dfUA7aLwSeyX7CbkS8BngNwKJFiyosIz/GenaHhkcyv3ffwHZGi0Xm9HY97ty82d1s2GzPriRJkqT6VmnYfQrw2ZTSa8cORMRCStsPnV5+nTaBOva23HDa4/2/Am9PKY3ub3XilNLFwMUAy5cvT11djw90ebO3Gnu6S8eamlr2er4aazcMALDwsHmPu/dh82dz34NrM39mvZnpv/68sl3yxzbJJ9slf2yTfLJd8sc2yad6bZdKw24fpSHLu6WUVlPqib2yijpWU9rWaMxCYO0e1ywHLi0H3bnA+RExklL6ZhXPza3xqzFnbePmUtjdc84uwPw53Vx7492ZP1OSJEmSplKlk0EvB542CXXcABwbEUsiogW4iD3Cc0ppSUrpyJTSkcDXgT+frkEXSvvswuQsULVxc2ns/bw5ewu7PQxu3cHOXZOzMJYkSZIkTYVKw+4ngFMi4g+yLCKlNAK8gdIqy3cDl6WU7oyI10XE67J8Vr0otJQ63Scj7I7NyZ076/Fhd3Z5Hm/fwNbMnytJkiRJU6XSYcz3AtuBr5QD72XA9SmlldUWklK6Grh6j2Of3se1r6j2eXk3mVsPbdg8QEtzE92dbY87N6unA4DNfVs5dN6szJ8tSZIkSVOh0rD7IWAZpVWYX1B+pYjoozSXd2wLossyq3CGap3EsLulfxuzezvZ20Jfs3o6y9fYsytJkiSpflUUdlNKbx/7vrwV0GmUgu/Y61xKqygbdqvU0jw2jDn7Baq2DGylt7tzr+dml8PuZsOuJEmSpDpWac/ubimlNcAa4H/HjkXELEqhV1XavUDVJCwU1T+wjd7u9r2em9Vb7tntM+xKkiRJql+VLlBFRMyJiHMi4ukRMX/8uZTSlpTSD7Irb+aazDm7W/q37R6uvKfervKcXXt2JUmSJNWxinp2I+JC4BKgfdyxtTw2X/dm4OZyr6+qMJlht29wG73dHXs919TUSHdnO30D2zJ/riRJkiRNlUqHMf8zsBP4W2AAOJHSvN2nAheUr0lAY1YFzlSPzdnNNuymlOjr33fYBZjd28lmhzFLkiRJqmOVht1FwLtSSh/f80REHAGcTmm1ZlWpsbGB5qbGzBeo2rZjF8Mjo8zaT9id1dPhasySJEmS6lqlYfdu9jHPN6W0ClgFXF5tUSoptDQzNJxtz+7Y8OT99uz2dLJuY1+mz5UkSZKkqVTpAlUfA14aEQ5TngKFlmZ27cq2Z7evvxx2e/bTs9vb6WrMkiRJkupaRWE3pfRl4Frg8oiYMzklaUyhpSnzObsH07M7q7uTLS5QJUmSJKmOVboa8wJgMaXFqNZGxA+B6ymtwnyTqzBnq7XQwo5dQ5nec8tAqcd2/3N2O9mxc4gdO4doa23J9PmSJEmSNBUqnbP7BeBZwK3AFuBU4DmUVmAmIjZSCr3nZ1jjjNXa2sLOXRn37O4exrz3fXahtBozwJb+rbS1zs70+ZIkSZI0FSoNu08BPptSeu3YgYhYSGn7odPLr9OyK29ma2ttYefObHt2x4Yx93S17/OaWeUgvLl/K4cfYtiVJEmSVH8qDbt9lIYs75ZSWg2sBq7MqCaVtU3KMOZtdLa37t7Hd29m9zzWsytJkiRJ9ajS1ZgvB542GYXo8VpbW9gxCT27PfuZrwulfXYBNrsisyRJkqQ6VWnY/QRwSkT8wWQUo9/UVpicYcz7W5wKHhvG3OeKzJIkSZLqVKVh917gKOArEXF5RFwUEUdmX5agNGc382HM/Vv3u+0QlObzRoQ9u5IkSZLqVqVzdj8ELKO0CvMLyq8UEX2U5vKObUF0WWYVzmBtrc2ZD2PuH9jOgkP3v0VyU1MjPV3tztmVJEmSVLcqCrsppbePfV/ec/c0SsF37HUupW2IDLsZaC20sH3nrkzvuWVgK71d++/ZhdIiVZsNu5IkSZLqVKU9u7ullNYAa4D/HTsWEbMohV5loK21haGhEUZHizQ2Vjri/PGKxSL9g9t3L0C1P709HWxxGLMkSZKkOlVRgoqIj0ZEz77Op5S2pJR+UH1ZglLYBdiZ0bzdwa07KBYTvQcRdu3ZlSRJklTPKu0u/HPg/oh4bUTEZBSkx7QVSmE3q0WqtpRXVz6YYcyzejpdjVmSJElS3ao07J4M3Aj8O3BLRJyddUF6TGu5ZzerRarGwuvY1kL7M7u3k819W0kpZfJsSZIkSZpKFYXdlNK9KaXzgQuANuD7EfH1iDhiUqqb4XYPY84o7G7pL4Xdnu72A17b293BrqHhzFeDliRJkqSpMKFVj1JK3wKeALwdeBZwd0S8LyIOPD5WBy3rYcz9g+We3e4D9+yO9f6OBWRJkiRJqicTXuI3pTSSUvowcCzwFUrB976IeFlWxc10bRkPYx4Lrr3dBzdnt/QZF6mSJEmSVH+q388GZgE/Aq4FDgO+GBHXR8QZGdx7Rst6zu6Wga1EBD1dBx7GPLY90ZYBw64kSZKk+lPRPrsRcSjwpHGv5cDYVkQJuAP4JXA2cF1EfAR4R3KVowkZG8ac1dZD/QPb6OpoO6g9e2eVe38dxixJkiSpHlUUdoG1lEJtAJuBnwPXA9cBv0gpbQWIiCbgr4H3lK9/R1YFzyRZD2PuG9i+u8f2QHrLw5j7HMYsSZIkqQ5VGnYvphxwU0r37euilNII8P6I6AZegWF3QrKfs7v1oObrwmPzere4164kSZKkOlRR2E0pva7C+98GHFLhZ1SW/WrM2w867DY3NdLV0eowZkmSJEl1qaIFqiLi4xFxzR7HmiLi9PJ83j19G/jDagqcyVoz3me3b2DbQYddgN7uTvpcoEqSJElSHap0NeZzgYfG3kREUFqJ+ZfA6oh4//iLU0pbUkqXVlvkTNXS3ERDQ2S69VBv94FXYh4zq6fDnl1JkiRJdanSObsLgdvHvT8feApwCVAE3hYRP0spXZVRfTNaRNBWaMlkGPPoaJGBrdvp7e486M/0dne4z64kSZKkulRp2E3A9nHvLwRWAi9PKaWImA28GTDsZqStrcCOncNV32dga6nZKhnGPLu3kwcfXl/1syVJkiRpqlU6jHkVsBR2D2G+ALhi3D663x47r2y0FVrYsXNX1ffpK6+qXMkwZufsSpIkSapXlfbsXga8NSKuBp4MzAeuHne+CMzOqDYB7W0tbN9Rfdgdm3tbSc/urJ4OBrftZHhklOamxqprkCRJkqSpUmnY/Tjw+8B3gABuBb437vwxwIZMKhMA7W2FTMJu/+BY2D34ObuzysG4b2Ab82Z3V12DJEmSJE2VSvfZHYyIMyjN1e0Fvj5uCDPl47dlV54621vZun1n1feZ0DDmnlIw7uvfatiVJEmSVFcq7dklpTQE/PeexyNiLnAtv9nTqyq1txVYv6m/6vtMdBgzwJYBtx+SJEmSVF8qDrv7klLaCLwiq/uppKOtla3bM1iganAbEUF3ZwX77JaHPLvXriRJkqR6U+lqzJMmIs6LiHsj4oGIeMdezr80In5Vfv08Ik6pRZ1TraO9wPYd1Q9j7h/YRndnG42NB9/kvWM9u+61K0mSJKnO5CLsRkQj8EngeZS2LnpJROy5hdGDwDNSSicD7wUuntoqa6O9rcC2DHp2t/Rvq2gIM8DsnrGeXcOuJEmSpPqSi7ALPAl4IKW0ojwn+FJKi13tllL6eUppS/nt9cDCKa6xJjrbWxkaHmFoeKSq+/QNVB5221pbaGlp2r24lSRJkiTVi8zm7FZpAfDwuPerKe3juy+vAv7vQDctFosMDg5WWdrkOZjaxkYdr9+wiZ6ug59vu6fNfYP0dLdX/PvR29XO+o19uf59zNJM+XXWG9slf2yTfLJd8sc2ySfbJX9sk3yq93bJS89u7OVY2ssxIuIcSmH37fs4/5qIuDEibty4cWOGJdZGR3sBoOq9dvsHt9NTweJUY3q6OugbtGdXkiRJUn3JS8/uamDRuPcLgbV7XhQRJwOfA56XUtq0txullC6mPJ93+fLlqaurK/tqM7a/GmfP6il9E037ve5A+gd3MG9OT8X3mDOri63bdlX17Ho003699cJ2yR/bJJ9sl/yxTfLJdskf2ySf6rVd8tKzewNwbEQsiYgW4CLgyvEXRMRi4HLgZSml+2pQY010trcCsK2Knt3R0SIDW7fTW95KqBKzejrdZ1eSJElS3clFz25KaSQi3gB8G2gEPp9SujMiXlc+/2ng74A5wKciAmAkpbS8VjVPlfa20jDmbdsnvv3QwNbtABUvUDX2mT5XY5YkSZJUZ3IRdgFSSlcDV+9x7NPjvn818OqprqvWOjLo2d3SX+qZ7e2ufM7urJ4OtgxsI6VE+YcMkiRJkpR7eRnGrH3oyKBnd2zroIkMY57d01keBr1jws+XJEmSpKlm2M25LHp2+wfHwm7lw5hn95Ymo2/uq+9lxyVJkiTNLIbdnMu2Z7fyYcxzZo2F3cmft7tj5xBDwyOT/hxJkiRJ059hN+faWluIiKr22X1szm7lPbtjYXfjlsnt2b31rgdZfsFf8YRnv4n/+fb1k/osSZIkSdOfYTfnGhoaaG9tYWs1PbuD24gIujsn0LNbHsa8acvAhJ9/INt37OLP/99n6O3p5KTjF/Ouj3yVR9ZvmbTnSZIkSZr+DLt1oL29UFXPbv/ANro722hsrLy5Z/eWFrXaNIk9u//3o5tZu34LH3zHy/jY372KoeERPve1707a8yRJkiRNf4bdOtDZ1lpVz+7mvm3M6ql8JWaAQkszXZ1tbJrEBaou+9bPOXLhfJ5y+gksXjCPc846iSu/dwMjI6OT9kxJkiRJ05thtw50dbYxMLh9wp/f3De4e+7tRMzt7Zq0ObuPrN/CL269j9973lm79/F94XOfzIZNA/zspnsm5ZmSJEmSpj/Dbh3o6Wqvap/bTX2Du4cjT8ScWV2TtvXQT2+4C4BnP/2U3cfOOeuJtLcV+N61t03KMyVJkiRNf4bdOtDd1V5Vz+7GLYPM7Z14z+6cWV2TNmf32hvuZu7sbo5bcvjuY4WWZp687Fh+dqM9u5IkSZImxrBbB3q6OuifYNgtFots6d/K7KrCbvekhN1iscjPbryHpy0/YfcQ5jFPXX4iKx5+lLWPbs78uZIkSZKmP8NuHejubKN/cBsppYo/2z+4ndHRYnVzdmd1sbl/K6OjxQnfY29+vWodm/oGecrpJzzu3NOWnwjgvF1JkiRJE2LYrQM9Xe2MjBbZsXOo4s9u6tsKUFXYnTOri2IxsWVg64TvsTe33bMKgFOXLnncueOPOpze7g5uuv3XmT5TkiRJ0sxg2K0DPV3tABMayrxpywAAc6oYxjx/Tg8AGzYNTPgee3P7PStpbytw1OJDH3cuIli2dAm33Lki02dKkiRJmhkMu3Wgp6sDmFjY3ZxBz+5Y2H10Y9+E77E3t929ipOOX0xj497/GJ76hCXc9+AjDG6b+ErUkiRJkmYmw24dGOvZHdhaedgd2x+3qp7duaWwu35j/4TvsafhkVHueuBhTj7+iH1es2zpElJK3F4e7ixJkiRJB8uwWwe6u9qAifbslsLurCr22Z2Mnt17V6xhaGiEk088cp/XLCufcyizJEmSpEoZdutANcOYN20ZpLe7g+amxgk/v9DSzKyeDh7NsGd3rLf2lP2E3Z7uDo5afAi33LUys+dKkiRJmhkMu3XgsQWqtlX82Y2bB6qarzvmkLm9PLqpr+r7jPnV3Svp6Wpn8eFz93vdqU84ilvvXDGhbZckSZIkzVyG3TrQ1VEaxjwwWPlCTes29nHo3N6qa5g/pyfTObu33bOKk084gojY73XLli5h45ZBVq/blNmzJUmSJE1/ht060NjYQFdH64SGMT+6sZ9DMgi7h8ztZf2mbMLuzl1D3LdiDU88Yd+LU4059QmlPXhvufPBTJ4tSZIkaWYw7NaJ7q4OBioMu8VikfUb+zhkXm/Vzz9kbg/rN/VTLBarvtdd969mZLTIySccecBrTzhqAa2FZhepkiRJklQRw26dmNXdweb+rRV9ZnP/VoZHRjmkvHVQNQ6Z28voaHH3VkbVuP3eAy9ONaapqZGTTziCW++yZ1eSJEnSwTPs1ol5c7rZsLmyYcRjqycfmkHP7uGHzAZgzbrNVd/rtrtXMnd290HXtWzpEu68/2GGhkeqfrYkSZKkmcGwWyfmz+lhw6aBij7z6Ia+8md7q37+osNKqyY//MjGqu91+z2rOOUgFqcas2zpEoaGRrj7gdVVP1uSJEnSzGDYrRPzZnezqW+Q0dGDnzP76MY+IJue3QWHlnp2qw27W7fv5IFV6w5qcaoxy5aOLVLlvF1JkiRJB8ewWyfmzelhdLRY0bzddRv6iAjmzal+zm5HeytzertY/Uh1WwDdce9DpJQOar7umMPmz+KQub3O25UkSZJ00Ay7dWJ+ObBuqGD7n0c39jFnVhfNTY2Z1LDwsDmsrrJn9/Z7SotTVdKzGxEsW3okt961sqpnS5IkSZo5DLt1Yt7sboCK9rpds24TC8oLS2Vh4WFzeLjKnt3b7lnJgkNmM3dWd0WfW7Z0CStXr2dzX2UrUldqZHSUa2+8h69ddS0rV6+f1GdJkiRJmjxNtS5AB2dsKPKGzQe/SNXK1Rs49QlLMqth0WFz+c5PbqVYLNLQMLGfk9x+zypOrmAI85ixebu33f0g55z1xAk9+0A2bhngT/7qk/zq3ocAaGps4O2vexF/+pJnT8rzJEmSJE0ee3brRKU9u0PDI6x5dBNHLJiXWQ2LDpvL8Mgoj6zvm9Dn+wa2sWrNBp54/MEPYR5z8glH0NAQ3HzH5CxStXPXMC9/68e5b+Uj/ONf/gE/+Mp7eNbTTuF9n/w6X/6fH0/KMyVJkiRNHsNunWhvK9DZ3nrQ2w+tWbeJYjFxxML5mdVwzJGHAnD/yrUT+vzYasrLlh5Z8Wc72ls56bjF/OLW+yb07AN5/6e+zp33PcyH3/kyLnz2GRy1+BD+7d1/yjOf8kTe/a+Xcuf9D0/KcyVJkiRNDsNuHSnttXtwPbur1mwA4IjDs+vZPW7J4QDct2JiYfeXtz1AU2MDpz7hqAl9/sxTj+OWOx9kx86hCX1+X267eyX/efmPecXvncMznrx09/GmpkY+8revYFZvJ3/9T19iZGQ00+dKkiRJmjyG3Tqy8LA5u0PsgewOuwuzC7uzejqZP6eHex+cWNi94bb7Oen4I2hrbZnQ58867XiGR0a56fZfT+jze5NS4t0f+xpzZ3fx1j+98HHnZ/V08p63vIS77n+Y/7riJ5k9V5IkSdLkMuzWkaMWH8qKhx8lpXTAa1euXk97W2H3XN+sHH/U4dy3Yk3Fn9u5a5hf3bOKJ51yzISffcYpx9LY2MDPbrpnwvfY0/d+9ituvmMFf/mq36Gro22v15z3jFN5+hkn8uHPXsHGLQe/QJgkSZKk2jHs1pGjjziU7Tt2sW5D3wGvfWDVOo5cOJ+IyLSG4446nPtXPsLoaLGiz9185wqGhkd40inHTvjZne2tLH/iMfzwutsnfI/xRkeLfPjib3LUokN48flP2ed1EcE/vOUidu4c4oOf/mYmz5YkSZI0uQy7deToI0oLRP161br9XpdSKm3xc0Llqx4fyAlHL2TnrmFWPLT/Gvb0w5/fTktzE2eddnxVz3/2007mnl+v4eFHNlZ1H4ArvvtL7l2xlrf+6YU0NTXu99qjFx/Kn/z+uVz2rZ9xy50PVv1sSZIkSZPLsFtHjl58CMABg+ZDazfSN7BtUsLuGSeXhiFff0tlqyL/8Po7ePKyY+lob63q+ec+9WQAvnftr6q6z85dQ3zks1dw0nGLed7Zpx7UZ974it/mkLm9/N2/fKXinm1JkiRJU8uwW0fmz+mhs72VXx8g7N5290oATj7xyMxrOGLBPA6bP4vrbr73oD+zas0GHlj5COec9cSqn79k0SGceMxCLr/muqru87lLv8eaRzfz/974YhoaDu6vQWd7K3/z+t/l9nsf4mtXXVvV8w9k3YYtXPm9G/jSN37It35w00HvryxJkiSppKnWBejgRQTHLjmMO+/b/56vt9+zikJLM8cftWBSajjr1OP50S/uoFgsHlRQ/MY11xERPPe3Dq4H9UD+4PlP5R/+9Wvccd9DnHTc4oo//+jGPj51yTU87+zTOPPU4yr67O886wy+csVP+eBnvsnzzj6NWT2dFT9/f+66/2E+/Nkr+MHPf3NeckRw/jmn8ZY/uYBjjjws02dKkiRJ05E9u3XmactP5Ja7HqR/YNtez6eU+PEv7uSUpUfSfIB5qBP1lOUnsLlvK7fcdeC5q6OjRf77Wz/n6WecyIJDZ2fy/Bc+58kUWpr54td/MKHPf+DfL2dkZJR3/tmLKv5sRPDut1zE4LYdfPizV0zo+Xuzc9cw7//UN3j+q97HzXes4E2v/G2u+o+/5cb//RBXfu6dvPYPn8MPr7uDZ7/s3bzrI19hYOuOzJ4tSZIkTUeG3Tpz9pknMTpa5Kc33L3X83c/sJr7HlzLBeeeMWk1nPeMU+lsb+W/vnngfWev+v6NPLJ+Cxdd8LTMnt/T3cEfvfC3uPya67lvRWV7/l7x3V/yP9/+Ba/7o+eyeMHE9iA+4egFvPx3z+G/vvkTvvWDmyZ0j/Fuu3slF7zqfXzmK9/h93/7qfz40vfyl6/6HU46fjFzZ3Vz8glH8o4/exE/vex9vPx3z+aSb/6EZ//RP/B/P7r5oLahkiRJkmai3AxjjojzgI8BjcDnUkof2ON8lM+fD2wHXpFSunnKC62xZUuX0NvdwTU/uYXnn7v8cee/cc11NDU28NvnnD5pNXS2t/Ki887k0quu5a2vvnCfPbZbt+/kA5++nJOOW8x5z8hmCPOYN/zx+Vz2rZ/zV//0RS775F/RWmg54Geuu/le3vb+/+T0Jx7Nm17+21U9/22vfSG33b2St7z38zQ0BM87+7SK7zGwdQef+OK3+I/Lvsf8OT184UNv5JyzTtrn9XNmdfEPf3ERL3zumbzzg5fwZ//vMzzrqSfzjj//XY4pr9Sdhf7B7dx614PcdMevueWOFaxZt5ntO3fR1NTI/Dk9HLFgHsuWLmHZ0iWceMxCWppz838jkiRJ0m6Rh56hiGgE7gOeDawGbgBeklK6a9w15wNvpBR2nwx8LKX05P3dd/ny5enGG2+ctLqrNTg4CEBXV1dFn3v/p77BZ77yHf7zX97Mbz1p6e7jv7j1Pl765o9ywbPO4KPv+pNMa93TQ2s2cP4r/5GjFh/C5/759cyf0/Mb59dt2MKb3v0f3HT7r/naJ97K8vIqzln69k9u5bV/8++ceepxvP9tf8SSRYfs9br+gW186fIf8YkvfosjFs7nsn/7K2b37n2ubSVt0jewjVf+9Se45c4H+b3zz+JPXnwuJx6zcL97Gw+PjHL/g2u54ru/5CtX/ITBbTt5ye88nXf++e/S3dl2EL/qkpGRUb7w3z/gX/7jSnbsHOKZT3kiF5y7nDNPPZ7D5s866Pvs3DXMAysf4c77H+LWOx/kpjtWcP/KR0gp0dAQnHD0QpYsmk9HWyvDIyOs39jP/Ssf2b1gVqGlmVOWHsnyJx7NsqVLOOaIw1h8+NwDbuW0L6OjRbYMbGXj5kE2bRlgU99W+ge2sX7jFrZu30lzczMRQUNDA73d7czq7mRWbyezujvo7emkt7ud3q6OCT//QFJKjIwWGR4eYXh4BCIotDRTaGnKfE/rvJvo/39pctku+WOb5JPtkj+2ST7VQ7tExE0ppcf3ApKfsHsW8A8ppeeW378TIKX0/nHXfAb4UUrpq+X39wJnp5Qe2dd9TzvttPTjH/94UmuvxkT/8OzYOcTvv+GjrFq7kSUL59Ha2sLw8CgPrFrH4YfM4rJPvKWi4DRRP7juDt76T18mgCMWzKWpsRQwdg2P8PDa0j64//RXLznorX0m4srv3cg//ts32LFrmDmzupjd00lroYmUoJgSg1t3sHrdZlJKPPupT+Tv3/xierra93m/Sttk565hPnXJt7nkmz9leGSUjrYCc2Z10dlR2mKpOFqkmBLFYpEdu4ZZt76P0WKRhobg2U87mVe9+JmceMzEFxLb3LeVr33r51x61c/Z3LcVgLbWFubN7qa10ExjQwMNDUFDQ1AsloLayMgoI6Oj9A1sp39w++57dXW2ccoJR7Bs6ZEsO/EITjpu0V63ikop8ejGfm67ZxW33rWSW+9ayT2/XsPIuO2Yujpa6enqoKO9QEMERGm+c0MEY5lweHiU4ZGx1wg7dw7TN7h9n0OzW5qbaGgIUkqMjhZ/43l76mxvpaerjebmJpoaG2hsbKSxsYHGhtLDi8VEMSVS+ev478e+joyrbXyt+6qvuamRluYmCi1NNDc30dzURGNjKZg3NgSNjY00NESpTSJKzyo/m/Kf12IxkSjVsOe5x94nxkqIKP1PUPp9jfLvbxBEQ1A6PXauYfc149skgIaG0j2oILCPjo4C0Ng4OT9Y0MTYLvljm+ST7ZI/tkk+jY6O8g9vehEnHFP5orBTpbu7O/dh9/eA81JKry6/fxnw5JTSG8ZdcxXwgZTSteX33wfenlK6cY97vQZ4DcCiRYtOv/POO6foV1G5an5SsqV/G1/932u5f+U6du4apqmpkaXHLOCi5z+VWT0dWZe6Tw+t3ch/X30dq9ZuJBUTRNDU2MBRiw/hhc85g4WHzpn0GtZv6uf/fnwrDz68nk19WxkeGSmHqqCjvZUlC+dxzplP4ISjDxwqJ9omm/u28qNf3Mm9Kx5hy8A2BrfuKIXMci9kQ0PQ3NzEwkNns2TRfM5cdizzZndP6Ne7N8VikXtXPMJNd6xgzaOb2bh5kF3DwxRHi4wW0+6Vs5uaGmluLH3t7mpn/uxuFi+Yy4lHL2DRYXMOehumPW3fuYsHVq7jwYfXs3b9lt1Betv2naSUSPAb4Q0oB8LG0qu5kUJzM7N7Ox979XQyu6eDnq52glFampt2t0tKiR07h9gysI2+ge30DWyjf/Cxr2OvkZEio6OjjBSLjI6WXgSldokgysGzoSHKPcZjQTB+o7bmpvG1lr5vamokpcTw8Ai7hkYYGi6/yt8Pj4xSLBYZLRYpFhOjYzUUi6RiIhpi95/TUi2lwNkwFlIbYlwwfewHBWPvGff7WsrApfdjYThRCs/s8fufSm92B+ixa1Oxsn8LRsr/UdLkf5Tkiu2SP7ZJPtku+WOb5NPI6Chv/9Pnc9zRi2pdyj7VQ9h9MfDcPcLuk1JKbxx3zbeA9+8Rdt+WUtrnCkHTdRizJo9tkk+2S/7YJvlku+SPbZJPtkv+2Cb5VA/tsr9hzHlZjXk1MP7HBQuBPZfZPZhrJEmSJEnKTdi9ATg2IpZERAtwEXDlHtdcCfxxlJwJ9O9vvq4kSZIkaebKxZ4hKaWRiHgD8G1KWw99PqV0Z0S8rnz+08DVlFZifoDS1kOvrFW9kiRJkqR8y0XYBUgpXU0p0I4/9ulx3yfg9VNdlyRJkiSp/uRlGLMkSZIkSZkx7EqSJEmSph3DriRJkiRp2jHsSpIkSZKmHcOuJEmSJGnaMexKkiRJkqYdw64kSZIkadox7EqSJEmSph3DriRJkiRp2omUUq1rmDQRsQFYVes6DmAusLHWReg32Cb5ZLvkj22ST7ZL/tgm+WS75I9tkk95b5cjUkrz9nZiWofdehARN6aUlte6Dj3GNskn2yV/bJN8sl3yxzbJJ9slf2yTfKrndnEYsyRJkiRp2jHsSpIkSZKmHcNu7V1c6wL0OLZJPtku+WOb5JPtkj+2ST7ZLvljm+RT3baLc3YlSZIkSdOOPbuSJEmSpGnHsFsjEXFeRNwbEQ9ExDtqXc9MFRGfj4j1EXHHuGOzI+K7EXF/+eusWtY400TEooj4YUTcHRF3RsSby8dtlxqKiNaI+GVE3FZul3eXj9suNRYRjRFxS0RcVX5vm9RYRKyMiNsj4taIuLF8zHapoYjojYivR8Q95X9fzrJNaisiji//HRl7DUTEX9gutRURbyn/O39HRHy1/O9/3baJYbcGIqIR+CTwPGAp8JKIWFrbqmasLwLn7XHsHcD3U0rHAt8vv9fUGQHemlI6ETgTeH3574ftUlu7gGemlE4BlgHnRcSZ2C558Gbg7nHvbZN8OCeltGzcdh22S219DLgmpXQCcAqlvzO2SQ2llO4t/x1ZBpwObAf+B9ulZiJiAfAmYHlK6SSgEbiIOm4Tw25tPAl4IKW0IqU0BFwKXFjjmmaklNJPgM17HL4Q+FL5+y8BL5jKmma6lNIjKaWby98PUvoPkgXYLjWVSraW3zaXXwnbpaYiYiHw28Dnxh22TfLJdqmRiOgGfgv4D4CU0lBKqQ/bJE/OBX6dUlqF7VJrTUBbRDQB7cBa6rhNDLu1sQB4eNz71eVjyodDUkqPQCl4AfNrXM+MFRFHAqcCv8B2qbnycNlbgfXAd1NKtkvt/SvwNqA47phtUnsJ+E5E3BQRrykfs11q5yhgA/CF8pD/z0VEB7ZJnlwEfLX8ve1SIymlNcCHgYeAR4D+lNJ3qOM2MezWRuzlmMtiS+NERCfwDeAvUkoDta5HkFIaLQ83Wwg8KSJOqnFJM1pEPB9Yn1K6qda16HGemlI6jdJ0pddHxG/VuqAZrgk4Dfj3lNKpwDbqaBjmdBcRLcDvAP9d61pmuvJc3AuBJcDhQEdE/FFtq6qOYbc2VgOLxr1fSGmIgPLh0Yg4DKD8dX2N65lxIqKZUtD9r5TS5eXDtktOlIf//YjSfHfbpXaeCvxORKykNB3mmRFxCbZJzaWU1pa/rqc0B/FJ2C61tBpYXR6NAvB1SuHXNsmH5wE3p5QeLb+3XWrnWcCDKaUNKaVh4HLgKdRxmxh2a+MG4NiIWFL+adZFwJU1rkmPuRJ4efn7lwNX1LCWGScigtK8qrtTSv8y7pTtUkMRMS8iesvft1H6B/EebJeaSSm9M6W0MKV0JKV/R36QUvojbJOaioiOiOga+x54DnAHtkvNpJTWAQ9HxPHlQ+cCd2Gb5MVLeGwIM9gutfQQcGZEtJf/e+xcSmun1G2bREqOnq2FiDif0lyrRuDzKaX31baimSkivgqcDcwFHgX+HvgmcBmwmNJf+henlPZcxEqTJCKeBvwUuJ3H5iH+DaV5u7ZLjUTEyZQWpWik9IPSy1JK74mIOdguNRcRZwN/lVJ6vm1SWxFxFKXeXCgNn/1KSul9tkttRcQySgu5tQArgFdS/v8ybJOaiYh2SuvYHJVS6i8f8+9KDZW3FvwDSrtj3AK8GuikTtvEsCtJkiRJmnYcxixJkiRJmnYMu5IkSZKkacewK0mSJEmadgy7kiRJkqRpx7ArSZIkSZp2DLuSJEmSpGnHsCtJkiRJmnYMu5Ik5VhEvDIi3rSf85+MiDUREVNZlyRJeWfYlSQp3z4IPHtvJ8oB90LgipRSmtKqJEnKOcOuJEk5FRHHAHOB6/dxyRnAAuCbU1WTJEn1wrArSVIORcQ3gfvLb/8xIlL59d5xl70Q6Ad+ONX1SZKUd021LkCSJO3VxUAj8Hzgz4Ct5ePXjbvmhcC3UkrDU1ybJEm5F07xkSQpnyLiCuCslNL8vZw7EbgLeHFK6etTXpwkSTlnz64kSfl1GnDLPs69ANgFXLO3kxHRC/xFBc/6eEppcwXXS5KUa4ZdSZJyKCLmAguBS/ZxyQuB76aUtu7jfC/w9xU88hLAsCtJmjYMu5Ik5dPp5a8373kiIhYCy4E/3deHU0orAffelSTNWK7GLElSPp1a/vq4sEtpCHMCrpyyaiRJqjOGXUmS8umo8teH9nLuhcC1KaUNU1iPJEl1xWHMkiTl04ry149HxHXAKPAVSnNxfwt4W43qkiSpLrj1kCRJORQR7cCngecBc4GHUkpHRMQfA18CjkopPVjLGiVJyjPDriRJdSQi/gdYklJaVutaJEnKM4cxS5JUX64DPlvrIiRJyjt7diVJkiRJ046rMUuSJEmSph3DriRJkiRp2jHsSpIkSZKmHcOuJEmSJGnaMexKkiRJkqYdw64kSZIkadox7EqSJEmSpp3/Dxq7yf1CVC68AAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot symmetry norm over time\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$symmetry-norm/-$', fontsize=18)\n",
+ "plt.grid(color='black', linestyle='-', linewidth=0.1)\n",
+ "plt.plot(t_nd, symmetry_norm, color=(0.121, 0.231, 0.4))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# store results to file\n",
+ "import csv\n",
+ "with open(filename, 'w') as f:\n",
+ " writer = csv.writer(f, delimiter='\\t')\n",
+ " writer.writerows(zip(t_nd, a_nd, symmetry_norm))"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/lbmpy_tests/full_scenarios/phasefield_allen_cahn/phasefield-gravity-wave.ipynb b/lbmpy_tests/full_scenarios/phasefield_allen_cahn/phasefield-gravity-wave.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..451c8872115a524fa05f3df49a0025267c3aea76
--- /dev/null
+++ b/lbmpy_tests/full_scenarios/phasefield_allen_cahn/phasefield-gravity-wave.ipynb
@@ -0,0 +1,1216 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import os\n",
+ "\n",
+ "import time\n",
+ "from tqdm.notebook import tqdm\n",
+ "\n",
+ "import numpy as np\n",
+ "import math\n",
+ "\n",
+ "from pystencils.session import *\n",
+ "from lbmpy.session import *\n",
+ "\n",
+ "from pystencils.simp import sympy_cse\n",
+ "from pystencils.boundaries import BoundaryHandling\n",
+ "\n",
+ "from lbmpy.phasefield_allen_cahn.parameter_calculation import AllenCahnParameters\n",
+ "from lbmpy.phasefield_allen_cahn.contact_angle import ContactAngle\n",
+ "from lbmpy.phasefield_allen_cahn.kernel_equations import *\n",
+ "\n",
+ "from lbmpy.advanced_streaming import LBMPeriodicityHandling\n",
+ "from lbmpy.boundaries import NoSlip, LatticeBoltzmannBoundaryHandling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If `pycuda` is installed the simulation automatically runs on GPU"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "No pycuda installed\n"
+ ]
+ }
+ ],
+ "source": [
+ "try:\n",
+ " import pycuda\n",
+ "except ImportError:\n",
+ " pycuda = None\n",
+ " gpu = False\n",
+ " target = ps.Target.CPU\n",
+ " print('No pycuda installed')\n",
+ "\n",
+ "if pycuda:\n",
+ " gpu = True\n",
+ " target = ps.Target.GPU"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Gravity wave simulated with a phase-field model for immiscible fluids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Geometry Setup\n",
+ "\n",
+ "First of all the stencils for the phase-field LB step as well as the stencil for the hydrodynamic LB step are defined. According to the stencils the simulation runs either in 2D or 3D"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "stencil_phase = LBStencil(Stencil.D2Q9)\n",
+ "stencil_hydro = LBStencil(Stencil.D2Q9)\n",
+ "assert(stencil_hydro.D == stencil_phase.D)\n",
+ "\n",
+ "dimensions = stencil_phase.D"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "timesteps = 238800\n",
+ "Re = 10\n",
+ "Pe = 0.41876046901171776\n",
+ "Cn = 0.1\n",
+ "domain_width = 50\n",
+ "fluid_depth = 25.0\n",
+ "amplitude = 0.5\n",
+ "relaxation_rate_heavy = 1.99\n",
+ "mobility = 0.02\n",
+ "interface_width = 5\n",
+ "density_heavy = 1.0\n",
+ "density_light = 0.001\n",
+ "density_ratio = 1000\n",
+ "kinematic_viscosity_heavy = 0.0008375209380234356\n",
+ "kinematic_viscosity_light = 0.0008375209380234356\n",
+ "kinematic_viscosity_ratio = 1\n",
+ "dynamic_viscosity_heavy = 0.0008375209380234356\n",
+ "dynamic_viscosity_light = 8.375209380234357e-07\n",
+ "dynamic_viscosity_ratio = 1000.0\n",
+ "wavelength = 50\n",
+ "wavenumber = 0.12566370614359174\n",
+ "wave_frequency = 0.00033500837520937423\n",
+ "surface_tension = 0\n",
+ "gravitational_acceleration = -8.964447065459421e-07\n",
+ "data_extract_frequency = 298\n",
+ "vtk_output_frequency = 2985\n"
+ ]
+ }
+ ],
+ "source": [
+ "# user defined input\n",
+ "\n",
+ "Re = 10 # Reynolds number\n",
+ "domain_width = 50\n",
+ "fluid_depth = 0.5 * domain_width\n",
+ "amplitude = 0.01 * domain_width\n",
+ "relaxation_rate_heavy = 1.99\n",
+ "mobility = 0.02 # phase field mobility\n",
+ "interface_width = 5 # phase field interface width\n",
+ "density_heavy = 1.0 # density of heavy phase\n",
+ "density_ratio = 1000\n",
+ "density_light = density_heavy / density_ratio # density of light phase\n",
+ "kinematic_viscosity_ratio = 1\n",
+ "\n",
+ "kinematic_viscosity_heavy = 1 / 3 * (1 / relaxation_rate_heavy - 0.5)\n",
+ "kinematic_viscosity_light = kinematic_viscosity_heavy / kinematic_viscosity_ratio\n",
+ "wavelength = domain_width\n",
+ "wavenumber = 2.0 * np.pi / domain_width\n",
+ "wave_frequency = Re * kinematic_viscosity_heavy / domain_width / amplitude # angular wave frequency\n",
+ "surface_tension = 0\n",
+ "gravitational_acceleration = - wave_frequency**2 / wavenumber / np.tanh(wavenumber * fluid_depth)\n",
+ "Pe = domain_width * amplitude * wave_frequency / mobility # Peclet number\n",
+ "Cn = interface_width / domain_width # Cahn number\n",
+ "dynamic_viscosity_heavy = kinematic_viscosity_heavy * density_heavy\n",
+ "relaxation_time_heavy = 3.0 * kinematic_viscosity_heavy\n",
+ "kinematic_viscosity_light = kinematic_viscosity_heavy / kinematic_viscosity_ratio\n",
+ "dynamic_viscosity_light = kinematic_viscosity_light * density_light\n",
+ "relaxation_time_light = 3.0 * kinematic_viscosity_light\n",
+ "\n",
+ "timesteps = int(80 / wave_frequency)\n",
+ "\n",
+ "data_extract_frequency = int(0.1 / wave_frequency)\n",
+ "vtk_output_frequency = int(1 / wave_frequency)\n",
+ "vtk_output_path = \"vtk_out/gravity-wave\"\n",
+ "vtk_base_directory = vtk_output_path.split(\"/\")[0] # create directory for vtk-output if it does not yet exist\n",
+ "if not os.path.exists(vtk_base_directory):\n",
+ " os.mkdir(os.getcwd() + \"/\" + vtk_base_directory)\n",
+ "\n",
+ "domain_size = (domain_width, domain_width)\n",
+ "filename = \"pf-re-\" + str(Re) + \"-resolution-\" + str(domain_width) + \".txt\"\n",
+ "\n",
+ "print(\"timesteps =\", timesteps)\n",
+ "print(\"Re =\", Re)\n",
+ "print(\"Pe =\", Pe)\n",
+ "print(\"Cn =\", Cn)\n",
+ "print(\"domain_width =\", domain_width)\n",
+ "print(\"fluid_depth =\", fluid_depth)\n",
+ "print(\"amplitude =\", amplitude)\n",
+ "print(\"relaxation_rate_heavy =\", relaxation_rate_heavy)\n",
+ "print(\"mobility =\", mobility)\n",
+ "print(\"interface_width =\", interface_width)\n",
+ "print(\"density_heavy =\", density_heavy)\n",
+ "print(\"density_light =\", density_light)\n",
+ "print(\"density_ratio =\", density_ratio)\n",
+ "print(\"kinematic_viscosity_heavy =\", kinematic_viscosity_heavy)\n",
+ "print(\"kinematic_viscosity_light =\", kinematic_viscosity_light)\n",
+ "print(\"kinematic_viscosity_ratio =\", kinematic_viscosity_ratio)\n",
+ "print(\"dynamic_viscosity_heavy =\", dynamic_viscosity_heavy)\n",
+ "print(\"dynamic_viscosity_light =\", dynamic_viscosity_light)\n",
+ "print(\"dynamic_viscosity_ratio =\", dynamic_viscosity_heavy/dynamic_viscosity_light)\n",
+ "print(\"wavelength =\", wavelength)\n",
+ "print(\"wavenumber =\", wavenumber)\n",
+ "print(\"wave_frequency =\", wave_frequency)\n",
+ "print(\"surface_tension =\", surface_tension)\n",
+ "print(\"gravitational_acceleration =\", gravitational_acceleration)\n",
+ "print(\"data_extract_frequency =\", data_extract_frequency)\n",
+ "print(\"vtk_output_frequency =\", vtk_output_frequency)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "parameters = AllenCahnParameters(density_heavy=density_heavy, density_light=density_light,\n",
+ " dynamic_viscosity_heavy=dynamic_viscosity_heavy,\n",
+ " dynamic_viscosity_light=dynamic_viscosity_light,\n",
+ " gravitational_acceleration=gravitational_acceleration,\n",
+ " surface_tension=surface_tension, mobility=mobility,\n",
+ " interface_thickness=interface_width)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <table style=\"border:none; width: 100%\">\n",
+ " <tr style=\"border:none\">\n",
+ " <th style=\"border:none\" >Name</th>\n",
+ " <th style=\"border:none\" >SymPy Symbol </th>\n",
+ " <th style=\"border:none\" >Value</th>\n",
+ " </tr>\n",
+ " <tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Density heavy phase</td>\n",
+ " <td style=\"border:none\">$\\rho_{H}$</td>\n",
+ " <td style=\"border:none\">$1.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Density light phase</td>\n",
+ " <td style=\"border:none\">$\\rho_{L}$</td>\n",
+ " <td style=\"border:none\">$0.001$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation time heavy phase</td>\n",
+ " <td style=\"border:none\">$\\tau_{H}$</td>\n",
+ " <td style=\"border:none\">$0.00251256281407031$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation time light phase</td>\n",
+ " <td style=\"border:none\">$\\tau_{L}$</td>\n",
+ " <td style=\"border:none\">$0.00251256281407031$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Relaxation rate Allen Cahn LB</td>\n",
+ " <td style=\"border:none\">$\\omega_{\\phi}$</td>\n",
+ " <td style=\"border:none\">$1.78571428571429$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Gravitational acceleration</td>\n",
+ " <td style=\"border:none\">$F_{g}$</td>\n",
+ " <td style=\"border:none\">$-8.96444706545942 \\cdot 10^{-7}$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Interface thickness</td>\n",
+ " <td style=\"border:none\">$W$</td>\n",
+ " <td style=\"border:none\">$5$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Mobility</td>\n",
+ " <td style=\"border:none\">$M_{m}$</td>\n",
+ " <td style=\"border:none\">$0.02$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">Surface tension</td>\n",
+ " <td style=\"border:none\">$\\sigma$</td>\n",
+ " <td style=\"border:none\">$0$</td>\n",
+ " </tr>\n",
+ "\n",
+ " </table>\n",
+ " "
+ ],
+ "text/plain": [
+ "<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x12d1bd550>"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "parameters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fields\n",
+ "\n",
+ "As a next step all fields which are needed get defined. To do so we create a `datahandling` object. More details about it can be found in the third tutorial of the [pystencils framework]( http://pycodegen.pages.walberla.net/pystencils/). Basically it holds all fields and manages the kernel runs."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create a datahandling object\n",
+ "dh = ps.create_data_handling((domain_size), periodicity=(True, False), parallel=False, default_target=target)\n",
+ "\n",
+ "# fields \n",
+ "g = dh.add_array(\"g\", values_per_cell=len(stencil_hydro))\n",
+ "dh.fill(\"g\", 0.0, ghost_layers=True)\n",
+ "h = dh.add_array(\"h\",values_per_cell=len(stencil_phase))\n",
+ "dh.fill(\"h\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "g_tmp = dh.add_array(\"g_tmp\", values_per_cell=len(stencil_hydro))\n",
+ "dh.fill(\"g_tmp\", 0.0, ghost_layers=True)\n",
+ "h_tmp = dh.add_array(\"h_tmp\",values_per_cell=len(stencil_phase))\n",
+ "dh.fill(\"h_tmp\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "u = dh.add_array(\"u\", values_per_cell=dh.dim)\n",
+ "dh.fill(\"u\", 0.0, ghost_layers=True)\n",
+ "\n",
+ "rho = dh.add_array(\"rho\", values_per_cell=1)\n",
+ "dh.fill(\"rho\", 1.0, ghost_layers=True)\n",
+ "\n",
+ "C = dh.add_array(\"C\")\n",
+ "dh.fill(\"C\", 0.0, ghost_layers=True)\n",
+ "C_tmp = dh.add_array(\"C_tmp\")\n",
+ "dh.fill(\"C_tmp\", 0.0, ghost_layers=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# set the frequency of the file outputs\n",
+ "vtk_writer = dh.create_vtk_writer(vtk_output_path, [\"C\", \"u\", \"rho\"], ghost_layers=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rho_L = parameters.symbolic_density_light\n",
+ "rho_H = parameters.symbolic_density_heavy\n",
+ "density = rho_L + C.center * (rho_H - rho_L)\n",
+ "\n",
+ "body_force = [0, 0, 0]\n",
+ "body_force[1] = parameters.symbolic_gravitational_acceleration * density"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Definition of the lattice Boltzmann methods"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "w_c = parameters.symbolic_omega_phi\n",
+ "\n",
+ "config_phase = LBMConfig(stencil=stencil_phase, method=Method.MRT, compressible=True,\n",
+ " delta_equilibrium=False,\n",
+ " force=sp.symbols(\"F_:2\"), velocity_input=u,\n",
+ " weighted=True, relaxation_rates=[0, w_c, w_c, 1, 1, 1, 1, 1, 1],\n",
+ " output={'density': C_tmp}, kernel_type='stream_pull_collide')\n",
+ "\n",
+ "method_phase = create_lb_method(lbm_config=config_phase)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "omega = parameters.omega(C)\n",
+ "config_hydro = LBMConfig(stencil=stencil_hydro, method=Method.MRT, compressible=False,\n",
+ " weighted=True, relaxation_rates=[omega, 1, 1, 1],\n",
+ " force=sp.symbols(\"F_:2\"),\n",
+ " output={'velocity': u}, kernel_type='collide_stream_push')\n",
+ "\n",
+ "method_hydro = create_lb_method(lbm_config=config_hydro)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <table style=\"border:none; width: 100%\">\n",
+ " <tr>\n",
+ " <th colspan=\"3\" style=\"text-align: left\">\n",
+ " Moment-Based Method\n",
+ " </th>\n",
+ " <td>Stencil: D2Q9</td>\n",
+ " <td>Zero-Centered Storage: ✓</td>\n",
+ " <td>Force Model: Guo</td>\n",
+ " </tr>\n",
+ " </table>\n",
+ " \n",
+ " <table style=\"border:none; width: 100%\">\n",
+ " <tr>\n",
+ " <th colspan=\"3\" style=\"text-align: left\">\n",
+ " Continuous Hydrodynamic Maxwellian Equilibrium\n",
+ " </th>\n",
+ " <td rowspan=\"2\" style=\"width: 50%; text-align: center\">\n",
+ " $f (\\rho, \\left( u_{0}, \\ u_{1}\\right), \\left( v_{0}, \\ v_{1}\\right)) \n",
+ " = \\frac{3 \\delta_{\\rho} e^{- \\frac{3 v_{0}^{2}}{2} - \\frac{3 v_{1}^{2}}{2}}}{2 \\pi} - \\frac{3 e^{- \\frac{3 v_{0}^{2}}{2} - \\frac{3 v_{1}^{2}}{2}}}{2 \\pi} + \\frac{3 e^{- \\frac{3 \\left(- u_{0} + v_{0}\\right)^{2}}{2} - \\frac{3 \\left(- u_{1} + v_{1}\\right)^{2}}{2}}}{2 \\pi}$\n",
+ " </td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <td>Compressible: ✗</td>\n",
+ " <td>Deviation Only: ✓</td>\n",
+ " <td>Order: 2</td>\n",
+ " </tr>\n",
+ " </table>\n",
+ " \n",
+ " <table style=\"border:none; width: 100%\">\n",
+ " <tr> <th colspan=\"3\" style=\"text-align: left\"> Relaxation Info </th> </tr>\n",
+ " <tr>\n",
+ " <th>Moment</th>\n",
+ " <th>Eq. Value </th>\n",
+ " <th>Relaxation Rate</th>\n",
+ " </tr>\n",
+ " <tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$1$</td>\n",
+ " <td style=\"border:none\">$\\delta_{\\rho}$</td>\n",
+ " <td style=\"border:none\">$0.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$x$</td>\n",
+ " <td style=\"border:none\">$u_{0}$</td>\n",
+ " <td style=\"border:none\">$0.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$y$</td>\n",
+ " <td style=\"border:none\">$u_{1}$</td>\n",
+ " <td style=\"border:none\">$0.0$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$x^{2} - y^{2}$</td>\n",
+ " <td style=\"border:none\">$u_{0}^{2} - u_{1}^{2}$</td>\n",
+ " <td style=\"border:none\">$\\frac{2}{2 {C}_{(0,0)} \\left(\\tau_{H} - \\tau_{L}\\right) + 2 \\tau_{L} + 1}$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$x y$</td>\n",
+ " <td style=\"border:none\">$u_{0} u_{1}$</td>\n",
+ " <td style=\"border:none\">$\\frac{2}{2 {C}_{(0,0)} \\left(\\tau_{H} - \\tau_{L}\\right) + 2 \\tau_{L} + 1}$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$3 x^{2} + 3 y^{2} - 2$</td>\n",
+ " <td style=\"border:none\">$3 u_{0}^{2} + 3 u_{1}^{2}$</td>\n",
+ " <td style=\"border:none\">$1$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$3 x^{2} y - y$</td>\n",
+ " <td style=\"border:none\">$0$</td>\n",
+ " <td style=\"border:none\">$1$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$3 x y^{2} - x$</td>\n",
+ " <td style=\"border:none\">$0$</td>\n",
+ " <td style=\"border:none\">$1$</td>\n",
+ " </tr>\n",
+ "<tr style=\"border:none\">\n",
+ " <td style=\"border:none\">$9 x^{2} y^{2} - 3 x^{2} - 3 y^{2} + 1$</td>\n",
+ " <td style=\"border:none\">$0$</td>\n",
+ " <td style=\"border:none\">$1$</td>\n",
+ " </tr>\n",
+ "</table>"
+ ],
+ "text/plain": [
+ "<lbmpy.methods.momentbased.momentbasedmethod.MomentBasedLbMethod at 0x12d4a1e50>"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "method_hydro"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Initialization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n",
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "h_updates = initializer_kernel_phase_field_lb(method_phase, C, u, h, parameters)\n",
+ "g_updates = initializer_kernel_hydro_lb(method_hydro, 1, u, g)\n",
+ "\n",
+ "h_init = ps.create_kernel(h_updates, target=dh.default_target, cpu_openmp=True).compile()\n",
+ "g_init = ps.create_kernel(g_updates, target=dh.default_target, cpu_openmp=True).compile()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# initialize the phase field\n",
+ "def initialize_phasefield():\n",
+ " Nx = domain_size[0]\n",
+ " Ny = domain_size[1]\n",
+ " \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False):\n",
+ " # get x as cell center coordinate, i.e., including shift with 0.5\n",
+ " x = np.zeros_like(block.midpoint_arrays[0])\n",
+ " x[:, :] = block.midpoint_arrays[0]\n",
+ " \n",
+ " # get y as cell center coordinate, i.e., including shift with 0.5\n",
+ " y = np.zeros_like(block.midpoint_arrays[1])\n",
+ " y[:, :] = block.midpoint_arrays[1] \n",
+ " \n",
+ " tmp = fluid_depth + amplitude * np.cos(x / (Nx - 1) * np.pi * 2 + np.pi)\n",
+ " \n",
+ " # initialize diffuse interface with tanh profile\n",
+ " init_values = 0.5 - 0.5 * np.tanh((y - tmp) / (interface_width / 2))\n",
+ " \n",
+ " block[\"C\"][:, :] = init_values\n",
+ " block[\"C_tmp\"][:, :] = init_values\n",
+ " \n",
+ " if gpu:\n",
+ " dh.all_to_gpu() \n",
+ " \n",
+ " dh.run_kernel(h_init, **parameters.symbolic_to_numeric_map)\n",
+ " dh.run_kernel(g_init)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot initial profile\n",
+ "x = np.arange(0, domain_size[0], 1) # start,stop,step\n",
+ "y = fluid_depth + amplitude * np.cos(x / (domain_size[0] - 1) * np.pi * 2 + np.pi)\n",
+ "\n",
+ "plt.plot(x,y, marker='o')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "initialize_phasefield()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scalar_field(dh.cpu_arrays[\"C\"])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot initial interface profile\n",
+ "x = np.arange(0, domain_size[1]+2, 1) # start,stop,step\n",
+ "y = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), :]\n",
+ "\n",
+ "plt.plot(x,y, marker='o')\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "force_h = interface_tracking_force(C, stencil_phase, parameters)\n",
+ "hydro_force = hydrodynamic_force(g, C, method_hydro, parameters, body_force)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Definition of the LB update rules"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "lbm_optimisation = LBMOptimisation(symbolic_field=h, symbolic_temporary_field=h_tmp)\n",
+ "allen_cahn_update_rule = create_lb_update_rule(lbm_config=config_phase,\n",
+ " lbm_optimisation=lbm_optimisation)\n",
+ "\n",
+ "allen_cahn_update_rule = add_interface_tracking_force(allen_cahn_update_rule, force_h)\n",
+ "\n",
+ "ast_kernel = ps.create_kernel(allen_cahn_update_rule, target=dh.default_target, cpu_openmp=True)\n",
+ "kernel_allen_cahn_lb = ast_kernel.compile()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[['spatialInner0'], ['spatialInner1']]\n"
+ ]
+ }
+ ],
+ "source": [
+ "force_Assignments = hydrodynamic_force_assignments(g, u, C, method_hydro, parameters, body_force)\n",
+ "\n",
+ "lbm_optimisation = LBMOptimisation(symbolic_field=g, symbolic_temporary_field=g_tmp)\n",
+ "hydro_lb_update_rule = create_lb_update_rule(lbm_config=config_hydro,\n",
+ " lbm_optimisation=lbm_optimisation)\n",
+ "\n",
+ "hydro_lb_update_rule = add_hydrodynamic_force(hydro_lb_update_rule, force_Assignments, C, g, parameters)\n",
+ "\n",
+ "ast_kernel = ps.create_kernel(hydro_lb_update_rule, target=dh.default_target, cpu_openmp=True)\n",
+ "kernel_hydro_lb = ast_kernel.compile()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Boundary Conditions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# periodic Boundarys for g, h and C\n",
+ "periodic_BC_C = dh.synchronization_function(C.name, target=dh.default_target, optimization = {\"openmp\": True})\n",
+ "\n",
+ "periodic_BC_g = LBMPeriodicityHandling(stencil=stencil_hydro, data_handling=dh, pdf_field_name=g.name,\n",
+ " streaming_pattern='push')\n",
+ "periodic_BC_h = LBMPeriodicityHandling(stencil=stencil_phase, data_handling=dh, pdf_field_name=h.name,\n",
+ " streaming_pattern='pull')\n",
+ "\n",
+ "# No slip boundary for the phasefield lbm\n",
+ "bh_allen_cahn = LatticeBoltzmannBoundaryHandling(method_phase, dh, 'h',\n",
+ " target=dh.default_target, name='boundary_handling_h',\n",
+ " streaming_pattern='pull')\n",
+ "\n",
+ "# No slip boundary for the velocityfield lbm\n",
+ "bh_hydro = LatticeBoltzmannBoundaryHandling(method_hydro, dh, 'g' ,\n",
+ " target=dh.default_target, name='boundary_handling_g',\n",
+ " streaming_pattern='push')\n",
+ "\n",
+ "contact_angle = BoundaryHandling(dh, C.name, stencil_hydro, target=dh.default_target)\n",
+ "contact = ContactAngle(90, interface_width)\n",
+ "\n",
+ "wall = NoSlip()\n",
+ "if dimensions == 2:\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, 0])\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, -1])\n",
+ "\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, 0])\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, -1])\n",
+ " \n",
+ " contact_angle.set_boundary(contact, make_slice[:, 0])\n",
+ " contact_angle.set_boundary(contact, make_slice[:, -1])\n",
+ "else:\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, 0, :])\n",
+ " bh_allen_cahn.set_boundary(wall, make_slice[:, -1, :])\n",
+ "\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, 0, :])\n",
+ " bh_hydro.set_boundary(wall, make_slice[:, -1, :])\n",
+ " \n",
+ " contact_angle.set_boundary(contact, make_slice[:, 0, :])\n",
+ " contact_angle.set_boundary(contact, make_slice[:, -1, :])\n",
+ "\n",
+ "\n",
+ "bh_allen_cahn.prepare()\n",
+ "bh_hydro.prepare()\n",
+ "contact_angle.prepare()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Full timestep"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# definition of the timestep for the immiscible fluids model\n",
+ "def timeloop():\n",
+ " # Solve the interface tracking LB step with boundary conditions\n",
+ " periodic_BC_h()\n",
+ " bh_allen_cahn() \n",
+ " dh.run_kernel(kernel_allen_cahn_lb, **parameters.symbolic_to_numeric_map)\n",
+ " dh.swap(\"C\", \"C_tmp\")\n",
+ " \n",
+ " # apply the three phase-phase contact angle\n",
+ " contact_angle()\n",
+ " # periodic BC of the phase-field\n",
+ " periodic_BC_C()\n",
+ " \n",
+ " # solve the hydro LB step with boundary conditions\n",
+ " dh.run_kernel(kernel_hydro_lb, **parameters.symbolic_to_numeric_map)\n",
+ " periodic_BC_g()\n",
+ " bh_hydro()\n",
+ " \n",
+ " # compute density (only for vtk output)\n",
+ " # must be done BEFORE swapping fields to avoid having outdated values\n",
+ " compute_density()\n",
+ " \n",
+ " # field swaps\n",
+ " dh.swap(\"h\", \"h_tmp\")\n",
+ " dh.swap(\"g\", \"g_tmp\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def initialize_hydrostatic_pressure(): \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False): \n",
+ " \n",
+ " # get y as cell center coordinate, i.e., including shift with 0.5\n",
+ " y = np.zeros_like(block.midpoint_arrays[1])\n",
+ " y[:, :] = block.midpoint_arrays[1]\n",
+ " \n",
+ " # compute hydrostatic density\n",
+ " rho_hydrostatic = 1 + 3 * gravitational_acceleration * (y - fluid_depth)\n",
+ " \n",
+ " # subtract 1 because PDFs in incompressible LBM are centered around zero in lbmpy\n",
+ " rho_hydrostatic -= 1\n",
+ "\n",
+ " # set equilibrium PDFs with velocity=0 and rho; \n",
+ " for i in range(0, stencil_hydro.Q, 1):\n",
+ " block[\"g\"][:,:,i] = method_hydro.weights[i] * rho_hydrostatic[:,:]\n",
+ " block[\"g_tmp\"][:,:,i] = method_hydro.weights[i] * rho_hydrostatic[:,:]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def compute_density(): \n",
+ " for block in dh.iterate(ghost_layers=True, inner_ghost_layers=False):\n",
+ " # PDFs in incompressible LBM are centered around zero in lbmpy\n",
+ " # => add 1 to whole sum, i.e., initialize with 1\n",
+ " block[\"rho\"].fill(1);\n",
+ " \n",
+ " # compute density\n",
+ " for i in range(block[\"g\"].shape[-1]):\n",
+ " block[\"rho\"][:,:] += block[\"g\"][:,:,i]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "if (gravitational_acceleration != 0):\n",
+ " initialize_hydrostatic_pressure()\n",
+ " compute_density()\n",
+ " plt.scalar_field(dh.cpu_arrays[\"rho\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "================================= start of the simulation ===================================\n"
+ ]
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "8c9dbae7a6154aabae39e76d60d326b2",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ " 0%| | 0/238800 [00:00<?, ?it/s]"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "\n",
+ "time needed for the calculation: 99.6110 seconds\n",
+ "MLUPS: 5.99\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"================================= start of the simulation ===================================\")\n",
+ "\n",
+ "start = time.time()\n",
+ "\n",
+ "pbar = tqdm(total=timesteps)\n",
+ "\n",
+ "timestep = []\n",
+ "surface_position = []\n",
+ "symmetry_norm = []\n",
+ "mass = []\n",
+ "\n",
+ "for i in range(0, timesteps):\n",
+ " \n",
+ " sum_c_2 = 0.0\n",
+ " sum_delta_c_2 = 0.0\n",
+ " \n",
+ " # write vtk output\n",
+ " if(i % vtk_output_frequency == 0):\n",
+ " if gpu:\n",
+ " dh.to_cpu(\"C\")\n",
+ " dh.to_cpu(\"u\")\n",
+ " dh.to_cpu(\"rho\")\n",
+ " vtk_writer(i)\n",
+ " \n",
+ " # extract data (to be written to file)\n",
+ " if(i % data_extract_frequency == 0):\n",
+ " pbar.update(data_extract_frequency)\n",
+ " \n",
+ " timestep.append(i)\n",
+ " \n",
+ " ny = domain_size[1]\n",
+ "\n",
+ " # get index containing phase field value < 0.5\n",
+ " i1 = np.argmax(dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), :] < 0.5)\n",
+ " i0 = i1 - 1 # index containing phase field value >= 0.5 \n",
+ "\n",
+ " f0 = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), i0] # phase field value >= 0.5\n",
+ " f1 = dh.cpu_arrays[\"C\"][int(domain_size[0] * 0.5), i1] # phase field value < 0.5\n",
+ "\n",
+ " # coordinate of cell center is index+0.5-1 (0.5 to get to cell center; -1 to remove ghost layer from index)\n",
+ " y0 = i0 + 0.5 - 1\n",
+ " y1 = i1 + 0.5 - 1\n",
+ "\n",
+ " #interpolate\n",
+ " surface_position.append( y0 + (y1 - y0) / (f1 - f0) * (0.5 - f0) )\n",
+ " \n",
+ " # evaluate symmetry in x-direction\n",
+ " for y in range(0, domain_size[1] - 1):\n",
+ " for x in range(0, domain_size[0] - 1):\n",
+ " if (x >= domain_size[0] * 0.5):\n",
+ " continue\n",
+ " \n",
+ " x_mirrored = domain_size[0] - 1 - x;\n",
+ " sum_c_2 += dh.cpu_arrays[\"C\"][x, y]**2\n",
+ " sum_delta_c_2 += (dh.cpu_arrays[\"C\"][x, y] - dh.cpu_arrays[\"C\"][x_mirrored, y])**2\n",
+ " \n",
+ " symmetry_norm.append( (sum_delta_c_2 / sum_c_2)**2 )\n",
+ " \n",
+ " mass.append(np.sum(dh.cpu_arrays[\"C\"]))\n",
+ " \n",
+ " timeloop()\n",
+ "\n",
+ "pbar.close()\n",
+ "end = time.time()\n",
+ "sim_time = end - start\n",
+ "print(\"\\n\")\n",
+ "print(\"time needed for the calculation: %4.4f\" % sim_time , \"seconds\")\n",
+ "\n",
+ "nrOfCells = np.prod(domain_size)\n",
+ "mlups = nrOfCells * timesteps / sim_time * 1e-6\n",
+ "\n",
+ "print(\"MLUPS: %4.2f\" % mlups)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "scrolled": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.image.AxesImage at 0x12db854f0>"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "if gpu:\n",
+ " dh.to_cpu(\"C\")\n",
+ " dh.to_cpu(\"u\")\n",
+ " dh.to_cpu(\"rho\")\n",
+ "\n",
+ "plt.scalar_field(dh.cpu_arrays[\"C\"])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# non-dimensionalize time and surface position\n",
+ "t_nd = [value * wave_frequency for value in timestep]\n",
+ "a_nd = [(value - fluid_depth) / amplitude for value in surface_position]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot(t_nd, mass, color=(0.121, 0.231, 0.4))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot surface position over time\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$a/-$', fontsize=18)\n",
+ "plt.grid(color='black', linestyle='-', linewidth=0.1)\n",
+ "plt.plot(t_nd, a_nd, color=(0.121, 0.231, 0.4))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot analytical solutions\n",
+ "x = 0.5 # position where surface elevation is evaluated;\n",
+ " # 0.5 means center of first cell;\n",
+ " # amplitude of analytical solution is at 0 (not in domain center)\n",
+ "\n",
+ "t = np.arange(0, timesteps, 1)\n",
+ "a = amplitude * np.exp(-2 * kinematic_viscosity_heavy * wavenumber**2 * t) # damping of wave amplitude\n",
+ "\n",
+ "# linear analytical solution\n",
+ "a_anal_lin = a * np.cos(wavenumber * x - wave_frequency * t) + fluid_depth\n",
+ "\n",
+ "# non-linear analytical solution\n",
+ "a_anal_nonlin = (a * np.cos(wavenumber * x - wave_frequency * t) + \n",
+ " wavenumber * a**2 * 0.5 * \n",
+ " (1 + 3 / (2 * np.sinh(wavenumber * fluid_depth)**2)) * \n",
+ " 1 / np.tanh(wavenumber * fluid_depth) * \n",
+ " np.cos(2 * wavenumber * x - 2 * wave_frequency * t) + fluid_depth)\n",
+ "\n",
+ "# non-dimesionalize time and surface position\n",
+ "a_anal_lin_nd = (a_anal_lin - fluid_depth) / amplitude\n",
+ "a_anal_nonlin_nd = (a_anal_nonlin - fluid_depth) / amplitude\n",
+ "t_anal_nd = t * wave_frequency\n",
+ "\n",
+ "plt.plot(t_anal_nd, a_anal_lin_nd, label=\"linear analytical solution\")\n",
+ "#plt.plot(t_anal_nd, a_anal_nonlin_nd, label=\"nonlinear analytical solution\")\n",
+ "plt.plot(t_nd, a_nd, label=\"simulation\")\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$a/-$', fontsize=18)\n",
+ "plt.legend()\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 1152x432 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot symmetry norm over time\n",
+ "plt.xlabel('$t/-$', fontsize=18)\n",
+ "plt.ylabel('$symmetry-norm/-$', fontsize=18)\n",
+ "plt.grid(color='black', linestyle='-', linewidth=0.1)\n",
+ "plt.plot(t_nd, symmetry_norm, color=(0.121, 0.231, 0.4))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# store results to file\n",
+ "import csv\n",
+ "with open(filename, 'w') as f:\n",
+ " writer = csv.writer(f, delimiter='\\t')\n",
+ " writer.writerows(zip(t_nd, a_nd, symmetry_norm))"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}