Commit 9b2ace20 authored by Markus Holzer's avatar Markus Holzer
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Update documentation

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%% Cell type:code id: tags:
``` python
from lbmpy.session import *
```
%% Cell type:markdown id: tags:
# Tutorial 03: Defining LB methods in *lbmpy*
## A) General Form
%% Cell type:markdown id: tags:
The lattice Boltzmann equation in its most general form is:
$$f_q(\mathbf{x} + \mathbf{c}_q \delta t, t+\delta t) = K\left( f_q(\mathbf{x}, t) \right)$$
with a discrete velocity set $\mathbf{c}_q$ (stencil) and a generic collision operator $K$.
So a lattice Boltzmann method can be fully defined by picking a stencil and a collision operator.
The collision operator $K$ has the following structure:
- Transformation of particle distribution function $f$ into collision space. This transformation has to be invertible and may be nonlinear.
- The collision operation is an convex combination of the pdf representation in collision space $c$ and some equilibrium vector $c^{(eq)}$. This equilibrium can also be defined in physical space, then $c^{(eq)} = C( f^{(eq)} ) $. The convex combination is done elementwise using a diagonal matrix $S$ where the diagonal entries are the relaxation rates.
- After collision, the collided state $c'$ is transformed back into physical space
![](../img/collision.svg)
The full collision operator is:
$$K(f) = C^{-1}\left( (I-S)C(f) + SC(f^{(eq}) \right)$$
or
$$K(f) = C^{-1}\left( C(f) - S (C(f) - C(f^{(eq})) \right)$$
%% Cell type:markdown id: tags:
## B) Moment-based relaxation
The most commonly used LBM collision operator is the multi relaxation time (MRT) collision.
In MRT methods the collision space is spanned by moments of the distribution function. This is a very natural approach, since the pdf moments are the quantities that go into the Chapman Enskog analysis that is used to show that LB methods can solve the Navier Stokes equations. Also the lower order moments correspond to the macroscopic quantities of interest (density/pressure, velocity, shear rates, heat flux). Furthermore the transformation to collision space is linear in this case, simplifying the collision equations:
$$K(f) = C^{-1}\left( C(f) - S (C(f) - C(f^{(eq})) \right)$$
$$K(f) = f - \underbrace{ C^{-1}SC}_{A}(f - f^{(eq)})$$
in *lbmpy* the following formulation is used, since it is more natural to define the equilibrium in moment-space instead of physical space:
$$K(f) = f - C^{-1}S(Cf - c^{(eq)})$$
%% Cell type:markdown id: tags:
### Use a pre-defined method
Lets create a moment-based method in *lbmpy* and see how the moment transformation $C$ and the relaxation rates that comprise the diagonal matrix $S$ can be defined. We start with a function that creates a basic MRT model.
Don't use this for real simulations, there orthogonalized MRT methods should be used, as discussed in the next section.
%% Cell type:code id: tags:
``` python
from lbmpy.creationfunctions import create_lb_method
method = create_lb_method(stencil='D2Q9', method='mrt_raw')
# check also method='srt', 'trt', 'mrt' or 'mrt3'
# check also method='srt', 'trt', 'mrt'
method
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fad71541198>
%% Cell type:markdown id: tags:
The first column labeled "Moment" defines the collision space and thus the transformation matrix $C$.
The remaining columns specify the equilibrium vector in moment space $c^{(eq)}$ and the corresponding relaxation rate.
Each row of the "Moment" column defines one row of $C$. In the next cells this matrix and the discrete velocity set (stencil) of our method are shown. Check for example the second last row of the table $x^2 y$: In the corresponding second last row of the moment matrix $C$ where each column stands for a lattice velocity (for ordering visualized stencil below) and each entry is the expression $x^2 y$ where $x$ and $y$ are the components of the lattice velocity.
In general the transformation matrix $C_{iq}$ is defined as;
$$c_i = C_{iq} f_q = \sum_q m_i(c_q)$$
where $m_i(c_q)$ is the $i$'th moment polynomial where $x$ and $y$ are substituted with the components of the $q$'th lattice velocity
%% Cell type:code id: tags:
``` python
# Transformation matrix C
method.moment_matrix
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle \left[\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\0 & 0 & 0 & -1 & 1 & -1 & 1 & -1 & 1\\0 & 1 & -1 & 0 & 0 & 1 & 1 & -1 & -1\\0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1\\0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1\\0 & 0 & 0 & 0 & 0 & -1 & 1 & 1 & -1\\0 & 0 & 0 & 0 & 0 & 1 & 1 & -1 & -1\\0 & 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\end{matrix}\right]$
⎡1 1 1 1 1 1 1 1 1 ⎤
⎢ ⎥
⎢0 0 0 -1 1 -1 1 -1 1 ⎥
⎢ ⎥
⎢0 1 -1 0 0 1 1 -1 -1⎥
⎢ ⎥
⎢0 0 0 1 1 1 1 1 1 ⎥
⎢ ⎥
⎢0 1 1 0 0 1 1 1 1 ⎥
⎢ ⎥
⎢0 0 0 0 0 -1 1 1 -1⎥
⎢ ⎥
⎢0 0 0 0 0 1 1 -1 -1⎥
⎢ ⎥
⎢0 0 0 0 0 -1 1 -1 1 ⎥
⎢ ⎥
⎣0 0 0 0 0 1 1 1 1 ⎦
%% Cell type:code id: tags:
``` python
ps.stencil.plot(method.stencil)
method.stencil
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle \left( \left( 0, \ 0\right), \ \left( 0, \ 1\right), \ \left( 0, \ -1\right), \ \left( -1, \ 0\right), \ \left( 1, \ 0\right), \ \left( -1, \ 1\right), \ \left( 1, \ 1\right), \ \left( -1, \ -1\right), \ \left( 1, \ -1\right)\right)$
((0, 0), (0, 1), (0, -1), (-1, 0), (1, 0), (-1, 1), (1, 1), (-1, -1), (1, -1))
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:markdown id: tags:
### Orthogonal MRTs
For a real MRT method, the moments should be orthogonalized.
One can either orthogonalize using the standard scalar product or a scalar product that is weighted with the lattice weights. If unsure, use the weighted version.
The next cell shows how to get both orthogonalized MRT versions in lbmpy.
%% Cell type:code id: tags:
``` python
weighted_ortho_mrt = create_lb_method(stencil="D2Q9", method="mrt", weighted=True)
weighted_ortho_mrt
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fad98775ba8>
%% Cell type:code id: tags:
``` python
ortho_mrt = create_lb_method(stencil="D2Q9", method="mrt", weighted=False)
ortho_mrt
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fad713c2e10>
%% Cell type:markdown id: tags:
One can check if a method is orthogonalized:
%% Cell type:code id: tags:
``` python
ortho_mrt.is_orthogonal, weighted_ortho_mrt.is_weighted_orthogonal
```
%%%% Output: execute_result
(True, True)
%% Cell type:markdown id: tags:
### Define custom MRT method
To choose custom values for the left moment column one can pass a nested list of moments.
Moments that should be relaxed with the same paramter are grouped together.
*lbmpy* also comes with a few templates for this list taken from literature:
%% Cell type:code id: tags:
``` python
from lbmpy.methods import mrt_orthogonal_modes_literature
from lbmpy.stencils import get_stencil
from lbmpy.moments import MOMENT_SYMBOLS
x, y, z = MOMENT_SYMBOLS
moments = mrt_orthogonal_modes_literature(get_stencil("D2Q9"), is_weighted=True, is_cumulant=False)
moments
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle \left[ \left[ 1\right], \ \left[ x, \ y\right], \ \left[ 3 x^{2} + 3 y^{2} - 2, \ x^{2} - y^{2}, \ x y\right], \ \left[ x \left(3 x^{2} + 3 y^{2} - 4\right), \ y \left(3 x^{2} + 3 y^{2} - 4\right)\right], \ \left[ - 15 x^{2} - 15 y^{2} + 9 \left(x^{2} + y^{2}\right)^{2} + 2\right]\right]$
⎢ ⎡ 2 2 2 2 ⎤ ⎡ ⎛ 2 2 ⎞ ⎛ 2
⎣[1], [x, y], ⎣3⋅x + 3⋅y - 2, x - y , x⋅y⎦, ⎣x⋅⎝3⋅x + 3⋅y - 4⎠, y⋅⎝3⋅x +
⎡ 2 ⎤⎤
2 ⎞⎤ ⎢ 2 2 ⎛ 2 2⎞ ⎥⎥
3⋅y - 4⎠⎦, ⎣- 15⋅x - 15⋅y + 9⋅⎝x + y ⎠ + 2⎦⎦
%% Cell type:markdown id: tags:
This nested moment list can be passed to `create_lb_method`:
%% Cell type:code id: tags:
``` python
create_lb_method(stencil="D2Q9", method="mrt", nested_moments=moments)
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fada8392588>
%% Cell type:markdown id: tags:
If one needs to also specify custom equilibrium moments the following approach can be used
%% Cell type:code id: tags:
``` python
rho = sp.symbols("rho")
u = sp.symbols("u_:3")
omega = sp.symbols("omega_:4")
method_table = [
# Conserved moments
(1, rho, 0 ),
(x, u[0], 0 ),
(y, u[1], 0 ),
# Shear moments
(x*y, u[0]*u[1], omega[0]),
(x**2-y**2, u[0]**2 - u[1]**2, omega[0]),
(x**2+y**2, 2*rho/3 + u[0]**2 + u[1]**2, omega[1]),
# Higher order
(x * y**2, u[0]/3, omega[2]),
(x**2 * y, u[1]/3, omega[2]),
(x**2 * y**2, rho/9 + u[0]**2/3 + u[1]**2/3, omega[3]),
]
method = create_generic_mrt(get_stencil("D2Q9"), method_table)
method
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fad70ef8978>
%% Cell type:markdown id: tags:
Instead of manually defining all entries in the method table, *lbmpy* has functions to fill the table according to a specific pattern. For example:
- for a full stencil (D2Q9, D3Q27) there exist exactly 9 or 27 linearly independent moments. These can either be taken as they are, or orthogonalized using Gram-Schmidt, weighted Gram-Schmidt or a Hermite approach
- equilibrium values can be computed from the standard discrete equilibrium of order 1,2 or 3. Alternatively they can also be computed as continuous moments of a Maxwellian distribution
One option is to start with one of *lbmpy*'s built-in methods and modify it with `create_lb_method_from_existing`.
In the next cell we fix the fourth order relaxation rate to a constant, by writing a function that defines how to alter each row of the collision table. This is for demonstration only, of course we could have done it right away when passing in the collision table.
%% Cell type:code id: tags:
``` python
def modification_func(moment, eq, rate):
if rate == omega[3]:
return moment, eq, 1.0
return moment, eq, rate
method = create_lb_method_from_existing(method, modification_func)
method
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7fad70f2db00>
%% Cell type:markdown id: tags:
Our customized method can be directly passed into one of the scenarios. We can for example set up a channel flow with it. Since we used symbols as relaxation rates, we have to pass them in as `kernel_params`.
%% Cell type:code id: tags:
``` python
ch = create_channel(domain_size=(100, 30), lb_method=method, u_max=0.05,
kernel_params={'omega_0': 1.8, 'omega_1': 1.4, 'omega_2': 1.5})
ch.run(500)
plt.vector_field(ch.velocity[:, :]);
```
%%%% Output: display_data
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)
%% Cell type:markdown id: tags:
#### Bonus: Automatic analysis
Above we have created a non-orthogonal MRT, where the shear viscosity and bulk viscosity can be independently controlled. For moment-based methods, *lbmpy* also offers an automatic Chapman Enskog analysis that can find the relation between viscosity and relaxation rate(s):
%% Cell type:code id: tags:
``` python
from lbmpy.chapman_enskog import ChapmanEnskogAnalysis
analysis = ChapmanEnskogAnalysis(method)
analysis.get_dynamic_viscosity()
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle - \frac{\omega_{0} - 2}{6 \omega_{0}}$
-(ω₀ - 2)
──────────
6⋅ω₀
%% Cell type:code id: tags:
``` python
analysis.get_bulk_viscosity()
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle - \frac{1}{9} - \frac{1}{3 \omega_{1}} + \frac{5}{9 \omega_{0}}$
1 1 5
- ─ - ──── + ────
9 3⋅ω₁ 9⋅ω₀
......
......@@ -58,8 +58,8 @@ General:
- ``velocity_input``: symbolic field where the velocities are read from (for advection diffusion LBM)
- ``density_input``: symbolic field or field access where to read density from. When passing this parameter,
``velocity_input`` has to be passed as well
- ``kernel_type``: supported values: 'stream_pull_collide' (default), 'collide_only'
- ``kernel_type``: supported values: 'stream_pull_collide' (default), 'collide_only', stream_pull_only,
collide_stream_push, esotwist_even, esotwist_odd, aa_even, aa_odd
Entropic methods:
......@@ -419,6 +419,9 @@ def create_lb_method(**params):
def relaxation_rate_getter(moments):
try:
if all(get_order(m) < 2 for m in moments):
if params['entropic']:
return relaxation_rates[0]
else:
return 0
res = relaxation_rates[next_relaxation_rate[0]]
next_relaxation_rate[0] += 1
......
......@@ -109,6 +109,13 @@ class MomentBasedLbMethod(AbstractLbMethod):
new_entry = RelaxationInfo(prev_entry[0], relaxation_rate)
self._momentToRelaxationInfoDict[e] = new_entry
def set_conserved_moments_relaxation_rate(self, relaxation_rate):
self.set_zeroth_moment_relaxation_rate(relaxation_rate)
self.set_first_moment_relaxation_rate(relaxation_rate)
def set_force_model(self, force_model):
self._forceModel = force_model
@property
def collision_matrix(self):
pdfs_to_moments = self.moment_matrix
......
from pystencils.field import Field
from lbmpy.creationfunctions import update_with_default_parameters
from lbmpy.fieldaccess import StreamPushTwoFieldsAccessor, CollideOnlyInplaceAccessor
from pystencils.fd.derivation import FiniteDifferenceStencilDerivation
......@@ -271,7 +270,7 @@ def interface_tracking_force(phi_field, stencil, interface_thickness, fd_stencil
return result
def get_update_rules_velocity(src_field, u_in, lb_method, force, density):
def get_update_rules_velocity(src_field, u_in, lb_method, force, density, sub_iterations=2):
r"""
Get assignments to update the velocity with a force shift
Args:
......@@ -280,6 +279,7 @@ def get_update_rules_velocity(src_field, u_in, lb_method, force, density):
lb_method: mrt lattice boltzmann method used for hydrodynamics
force: force acting on the hydrodynamic lb step
density: the interpolated density of the simulation
sub_iterations: number of updates of the velocity field
"""
stencil = lb_method.stencil
dimensions = len(stencil[0])
......@@ -298,25 +298,36 @@ def get_update_rules_velocity(src_field, u_in, lb_method, force, density):
update_u = list()
update_u.append(Assignment(sp.symbols("rho"), m0[0]))
index = 0
u_symp = sp.symbols("u_:{}".format(dimensions))
zw = sp.symbols("zw_:{}".format(dimensions))
aleph = sp.symbols("aleph_:{}".format(dimensions * sub_iterations))
for i in range(dimensions):
update_u.append(Assignment(aleph[i], u_in.center_vector[i]))
index += 1
for k in range(sub_iterations - 1):
subs_dict = dict(zip(u_symp, aleph[k * dimensions:index]))
for i in range(dimensions):
update_u.append(Assignment(zw[i], u_in.center_vector[i]))
update_u.append(Assignment(aleph[index], m0[indices[i]] + force[i].subs(subs_dict) / density / 2))
index += 1
subs_dict = dict(zip(u_symp, zw))
subs_dict = dict(zip(u_symp, aleph[index - dimensions:index]))
for i in range(dimensions):
update_u.append(Assignment(u_in.center_vector[i], m0[indices[i]] + force[i].subs(subs_dict) / density / 2))
update_u.append(Assignment(u_symp[i], m0[indices[i]] + force[i].subs(subs_dict) / density / 2))
# update_u.append(Assignment(u_in.center_vector[i], m0[indices[i]] + force[i].subs(subs_dict) / density / 2))
return update_u
def get_collision_assignments_hydro(density=1, optimization=None, **kwargs):
def get_collision_assignments_hydro(density=1, optimization=None, sub_iterations=2, **kwargs):
r"""
Get collision assignments for the hydrodynamic lattice Boltzmann step. Here the force gets applied in the moment
space. Afterwards the transformation back to the pdf space happens.
Args:
density: the interpolated density of the simulation
optimization: for details see createfunctions.py
sub_iterations: number of updates of the velocity field
"""
if optimization is None:
optimization = {}
......@@ -327,22 +338,11 @@ def get_collision_assignments_hydro(density=1, optimization=None, **kwargs):
stencil = lb_method.stencil
dimensions = len(stencil[0])
field_data_type = 'float64' if opt_params['double_precision'] else 'float32'
q = len(stencil)
u_in = params['velocity_input']
force = params['force']
if opt_params['symbolic_field'] is not None:
src_field = opt_params['symbolic_field']
else:
src_field = Field.create_generic(params['field_name'], spatial_dimensions=lb_method.dim,
index_shape=(q,), layout=opt_params['field_layout'], dtype=field_data_type)
if opt_params['symbolic_temporary_field'] is not None:
dst_field = opt_params['symbolic_temporary_field']
else:
dst_field = src_field.new_field_with_different_name(params['temporary_field_name'])
moment_matrix = lb_method.moment_matrix
rel = lb_method.relaxation_rates
......@@ -364,12 +364,9 @@ def get_collision_assignments_hydro(density=1, optimization=None, **kwargs):
m = sp.symbols("m_:{}".format(len(stencil)))
update_m = get_update_rules_velocity(src_field, u_in, lb_method, force, density)
update_m = get_update_rules_velocity(src_field, u_in, lb_method, force, density, sub_iterations=sub_iterations)
u_symp = sp.symbols("u_:{}".format(dimensions))
for i in range(dimensions):
update_m.append(Assignment(u_symp[i], u_in.center_vector[i]))
for i in range(0, len(stencil)):
update_m.append(Assignment(m[i], m0[i] - (m0[i] - eq[i] + mf[i] / 2) * rel[i] + mf[i]))
......@@ -385,6 +382,9 @@ def get_collision_assignments_hydro(density=1, optimization=None, **kwargs):
for i in range(0, len(stencil)):
update_g.append(Assignment(post_collision_accesses[i], var[i]))
for i in range(dimensions):
update_g.append(Assignment(u_in.center_vector[i], u_symp[i]))
hydro_lb_update_rule = AssignmentCollection(main_assignments=update_g,
subexpressions=update_m)
......
from collections import OrderedDict
import numpy as np
from lbmpy.creationfunctions import create_lb_method, create_lb_update_rule
from lbmpy.methods.creationfunctions import create_with_discrete_maxwellian_eq_moments
from lbmpy.phasefield_allen_cahn.analytical import analytic_rising_speed
from lbmpy.phasefield_allen_cahn.force_model import MultiphaseForceModel
from lbmpy.phasefield_allen_cahn.kernel_equations import (
......@@ -85,11 +82,9 @@ def test_codegen_3d():
method_phase = create_lb_method(stencil=stenc