07_tutorial_shanchen_twophase.ipynb 34 KB
 Michael Kuron committed Oct 18, 2019 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Shan-Chen Two-Phase Single-Component Lattice Boltzmann" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from lbmpy.session import *\n", "from lbmpy.updatekernels import create_stream_pull_with_output_kernel\n", Martin Bauer committed Oct 21, 2019 18 19 "from lbmpy.macroscopic_value_kernels import macroscopic_values_getter, macroscopic_values_setter\n", "from lbmpy.maxwellian_equilibrium import get_weights" Michael Kuron committed Oct 18, 2019 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is based on section 9.3.2 of Krüger et al.'s \"The Lattice Boltzmann Method\", Springer 2017 (http://www.lbmbook.com).\n", "Sample code is available at [https://github.com/lbm-principles-practice/code/](https://github.com/lbm-principles-practice/code/blob/master/chapter9/shanchen.cpp)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameters" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "N = 64\n", "omega_a = 1.\n", "g_aa = -4.7\n", Martin Bauer committed Oct 21, 2019 46 47 48 49 "rho0 = 1.\n", "\n", "stencil = get_stencil(\"D2Q9\")\n", "weights = get_weights(stencil, c_s_sq=sp.Rational(1,3))" Michael Kuron committed Oct 18, 2019 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data structures" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ Martin Bauer committed Oct 21, 2019 65 "dim = len(stencil[0])\n", Michael Kuron committed Oct 18, 2019 66 "\n", Martin Bauer committed Oct 21, 2019 67 "dh = ps.create_data_handling((N,)*dim, periodicity=True, default_target='cpu')\n", Michael Kuron committed Oct 18, 2019 68 "\n", Martin Bauer committed Oct 21, 2019 69 70 "src = dh.add_array('src', values_per_cell=len(stencil))\n", "dst = dh.add_array_like('dst', 'src')\n", Michael Kuron committed Oct 18, 2019 71 "\n", Martin Bauer committed Oct 21, 2019 72 "ρ = dh.add_array('rho')" Michael Kuron committed Oct 18, 2019 73 74 75 76 77 78 79 80 81 82 83 84 85 86 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Force & combined velocity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The force on the fluid is\n", Michael Kuron committed Dec 19, 2019 87 "$\\vec{F}_A(\\vec{x})=-\\psi(\\rho_A(\\vec{x}))g_{AA}\\sum\\limits_{i=1}^{q}w_i\\psi(\\rho_A(\\vec{x}+\\vec{c}_i))\\vec{c}_i$\n", Michael Kuron committed Oct 18, 2019 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 "with \n", "$\\psi(\\rho)=\\rho_0\\left[1-\\exp(-\\rho/\\rho_0)\\right]$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def psi(dens):\n", " return rho0 * (1. - sp.exp(-dens / rho0));" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "zero_vec = sp.Matrix([0] * dh.dim) \n", "\n", Martin Bauer committed Oct 21, 2019 110 111 "force = sum((psi(ρ[d]) * w_d * sp.Matrix(d)\n", " for d, w_d in zip(stencil, weights)), zero_vec) * psi(ρ.center) * -1 * g_aa" Michael Kuron committed Oct 18, 2019 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kernels" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ Martin Bauer committed Oct 21, 2019 127 128 129 130 131 132 133 134 135 136 "collision = create_lb_update_rule(stencil=stencil,\n", " relaxation_rate=omega_a, \n", " compressible=True,\n", " force_model='guo', \n", " force=force,\n", " kernel_type='collide_only',\n", " optimization={'symbolic_field': src})\n", "\n", "stream = create_stream_pull_with_output_kernel(collision.method, src, dst, {'density': ρ})\n", "\n", Michael Kuron committed Oct 18, 2019 137 "\n", Martin Bauer committed Oct 21, 2019 138 139 "opts = {'cpu_openmp': False, \n", " 'target': dh.default_target}\n", Michael Kuron committed Oct 18, 2019 140 "\n", Martin Bauer committed Oct 21, 2019 141 142 "stream_kernel = ps.create_kernel(stream, **opts).compile()\n", "collision_kernel = ps.create_kernel(collision, **opts).compile()" Michael Kuron committed Oct 18, 2019 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ Martin Bauer committed Oct 21, 2019 158 159 160 161 162 163 "method_without_force = create_lb_method(stencil=stencil, relaxation_rate=omega_a, compressible=True)\n", "init_assignments = macroscopic_values_setter(method_without_force, velocity=(0, 0), \n", " pdfs=src.center_vector, density=ρ.center)\n", "\n", "\n", "init_kernel = ps.create_kernel(init_assignments, ghost_layers=0).compile()" Michael Kuron committed Oct 18, 2019 164 165 166 167 168 169 170 171 172 173 174 175 ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def init():\n", " for x in range(N):\n", " for y in range(N):\n", " if (x-N/2)**2 + (y-N/2)**2 <= 15**2:\n", Martin Bauer committed Oct 21, 2019 176 " dh.fill(ρ.name, 2.1, slice_obj=[x,y])\n", Michael Kuron committed Oct 18, 2019 177 " else:\n", Martin Bauer committed Oct 21, 2019 178 " dh.fill(ρ.name, 0.15, slice_obj=[x,y])\n", Michael Kuron committed Oct 18, 2019 179 "\n", Martin Bauer committed Oct 21, 2019 180 " dh.run_kernel(init_kernel)" Michael Kuron committed Oct 18, 2019 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Timeloop" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ Martin Bauer committed Oct 21, 2019 196 197 "sync_pdfs = dh.synchronization_function([src.name])\n", "sync_ρs = dh.synchronization_function([ρ.name])\n", Michael Kuron committed Oct 18, 2019 198 199 200 201 202 "\n", "def time_loop(steps):\n", " dh.all_to_gpu()\n", " for i in range(steps):\n", " sync_ρs()\n", Martin Bauer committed Oct 21, 2019 203 " dh.run_kernel(collision_kernel)\n", Michael Kuron committed Oct 18, 2019 204 205 " \n", " sync_pdfs()\n", Martin Bauer committed Oct 21, 2019 206 " dh.run_kernel(stream_kernel)\n", Michael Kuron committed Oct 18, 2019 207 " \n", Martin Bauer committed Oct 21, 2019 208 " dh.swap(src.name, dst.name)\n", Michael Kuron committed Oct 18, 2019 209 210 211 212 213 " dh.all_to_cpu()" ] }, { "cell_type": "code", Martin Bauer committed Oct 21, 2019 214 "execution_count": 10, Michael Kuron committed Oct 18, 2019 215 216 217 218 "metadata": {}, "outputs": [], "source": [ "def plot_ρs():\n", Martin Bauer committed Oct 21, 2019 219 220 " plt.title(\"$\\\\rho$\")\n", " plt.scalar_field(dh.gather_array(ρ.name), vmin=0, vmax=2.5)\n", Michael Kuron committed Oct 18, 2019 221 222 223 224 225 226 227 228 229 230 231 232 233 " plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run the simulation\n", "### Initial state" ] }, { "cell_type": "code", Martin Bauer committed Oct 21, 2019 234 "execution_count": 11, Michael Kuron committed Oct 18, 2019 235 236 237 238 "metadata": {}, "outputs": [ { "data": { Martin Bauer committed Oct 21, 2019 239 "image/png": "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\n", Michael Kuron committed Oct 18, 2019 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 "text/plain": [ "