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Commit 78beeb86 authored by Martin Bauer's avatar Martin Bauer
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Merge branch 'shanchen' into 'master'

Shan-Chen tutorial

See merge request pycodegen/lbmpy!8
parents 835f8e4d 55512e7d
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%% Cell type:markdown id: tags:
# Shan-Chen Two-Phase Single-Component Lattice Boltzmann
%% Cell type:code id: tags:
``` python
from lbmpy.session import *
from lbmpy.updatekernels import create_stream_pull_with_output_kernel
from lbmpy.macroscopic_value_kernels import macroscopic_values_getter, macroscopic_values_setter
```
%% Cell type:markdown id: tags:
This is based on section 9.3.2 of Krüger et al.'s "The Lattice Boltzmann Method", Springer 2017 (http://www.lbmbook.com).
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 id: tags:
## Parameters
%% Cell type:code id: tags:
``` python
N = 64
omega_a = 1.
g_aa = -4.7
rho0 = 1.
```
%% Cell type:markdown id: tags:
## Data structures
%% Cell type:code id: tags:
``` python
dh = ps.create_data_handling((N, N), periodicity=True, default_target='cpu')
method_a = create_lb_method(relaxation_rate=omega_a, compressible=True)
src_a = dh.add_array('src_a', values_per_cell=len(method_a.stencil))
dst_a = dh.add_array_like('dst_a', 'src_a')
ρ_a = dh.add_array('rho_a')
```
%% Cell type:markdown id: tags:
## Force & combined velocity
%% Cell type:markdown id: tags:
The force on the fluid is
$\vec{F}_A(\vec{x})=-\psi(\rho_A(\vec{x}))g_{AA}\sum\limits_{i=1}^{19}w_i\psi(\rho_A(\vec{x}+\vec{c}_i))\vec{c}_i$
with
$\psi(\rho)=\rho_0\left[1-\exp(-\rho/\rho_0)\right]$.
%% Cell type:code id: tags:
``` python
def psi(dens):
return rho0 * (1. - sp.exp(-dens / rho0));
```
%% Cell type:code id: tags:
``` python
zero_vec = sp.Matrix([0] * dh.dim)
stencil, weights = method_a.stencil, method_a.weights
force_a = sum((psi(ρ_a[d]) * w_d * sp.Matrix(d)
for d, w_d in zip(stencil, weights)),
zero_vec) * psi(ρ_a.center) * -1 * g_aa
```
%% Cell type:markdown id: tags:
## Kernels
%% Cell type:code id: tags:
``` python
stream_a = create_stream_pull_with_output_kernel(method_a, src_a, dst_a, {'density': ρ_a})
# TODO use method above
collision_a = create_lb_update_rule(relaxation_rate=omega_a,
compressible=True,
force_model='guo',
force=force_a,
kernel_type='collide_only',
optimization={'symbolic_field': src_a})
opts = {'cpu_openmp': False}
stream_a_kernel = ps.create_kernel(stream_a, **opts).compile()
collision_a_kernel = ps.create_kernel(collision_a, **opts).compile()
```
%% Cell type:markdown id: tags:
## Initialization
%% Cell type:code id: tags:
``` python
init_a = macroscopic_values_setter(method_a, velocity=(0, 0),
pdfs=src_a.center_vector, density=ρ_a.center)
init_a_kernel = ps.create_kernel(init_a, ghost_layers=0).compile()
```
%% Cell type:code id: tags:
``` python
def init():
for x in range(N):
for y in range(N):
if (x-N/2)**2 + (y-N/2)**2 <= 15**2:
dh.fill(ρ_a.name, 2.1, slice_obj=[x,y])
else:
dh.fill(ρ_a.name, 0.15, slice_obj=[x,y])
dh.run_kernel(init_a_kernel)
```
%% Cell type:markdown id: tags:
## Timeloop
%% Cell type:code id: tags:
``` python
sync_pdfs = dh.synchronization_function([src_a.name])
sync_ρs = dh.synchronization_function([ρ_a.name])
def time_loop(steps):
dh.all_to_gpu()
for i in range(steps):
sync_ρs()
dh.run_kernel(collision_a_kernel)
sync_pdfs()
dh.run_kernel(stream_a_kernel)
dh.swap(src_a.name, dst_a.name)
dh.all_to_cpu()
```
%% Cell type:code id: tags:
``` python
def plot_ρs():
plt.title("$\\rho_A$")
plt.scalar_field(dh.gather_array(ρ_a.name), vmin=0, vmax=2.5)
plt.colorbar()
```
%% Cell type:markdown id: tags:
## Run the simulation
### Initial state
%% Cell type:code id: tags:
``` python
init()
plot_ρs()
```
%% Output
%% Cell type:markdown id: tags:
### Check the first time step against reference data
The reference data was obtained with the [sample code](https://github.com/lbm-principles-practice/code/blob/master/chapter9/shanchen.cpp) after making the following changes:
```c++
const int nsteps = 1000;
const int noutput = 1;
```
Remove the next cell if you changed the parameters at the beginning of this notebook.
%% Cell type:code id: tags:
``` python
init()
time_loop(1)
ref_a = np.array([0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.136756, 0.220324, 1.2382, 2.26247, 2.26183, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.26183, 2.26247, 1.2382, 0.220324, 0.136756, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15, 0.15])
assert np.allclose(dh.gather_array(ρ_a.name)[N//2], ref_a)
```
%% Cell type:markdown id: tags:
### Run the simulation until converged
%% Cell type:code id: tags:
``` python
init()
time_loop(1000)
plot_ρs()
```
%% Output
%% Cell type:code id: tags:
``` python
```
This diff is collapsed.
...@@ -14,6 +14,8 @@ You can open the notebooks directly to play around with the code examples. ...@@ -14,6 +14,8 @@ You can open the notebooks directly to play around with the code examples.
/notebooks/04_tutorial_nondimensionalization_and_scaling.ipynb /notebooks/04_tutorial_nondimensionalization_and_scaling.ipynb
/notebooks/05_tutorial_modifying_method_smagorinsky.ipynb /notebooks/05_tutorial_modifying_method_smagorinsky.ipynb
/notebooks/06_tutorial_thermal_lbm.ipynb /notebooks/06_tutorial_thermal_lbm.ipynb
/notebooks/07_tutorial_shanchen_twophase.ipynb
/notebooks/08_tutorial_shanchen_twocomponent.ipynb
/notebooks/demo_stencils.ipynb /notebooks/demo_stencils.ipynb
/notebooks/demo_create_method_from_scratch.ipynb /notebooks/demo_create_method_from_scratch.ipynb
/notebooks/demo_moments_cumulants_and_maxwellian_equilibrium.ipynb /notebooks/demo_moments_cumulants_and_maxwellian_equilibrium.ipynb
......
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