Commit ce96664e authored by Markus Holzer's avatar Markus Holzer
Browse files

Fix wrong factor

parent 21b1d786
Pipeline #39384 passed with stages
in 107 minutes and 53 seconds
%% Cell type:markdown id: tags:
# Casson model for simulating Non Newtonian blood flow
%% Cell type:code id: tags:
``` python
import math
from lbmpy.session import *
from lbmpy.non_newtonian_models import CassonsParameters
from lbmpy.relaxationrates import lattice_viscosity_from_relaxation_rate
```
%% Cell type:markdown id: tags:
The primary source for the implementation of the Casson model can be found [here](https://doi.org/10.1007/s10955-005-8415-x)
%% Cell type:code id: tags:
``` python
stencil = LBStencil(Stencil.D3Q27)
W = 41
L = 1 * W
domain_size = (L, W, W)
omega = 1.0
nu = lattice_viscosity_from_relaxation_rate(omega)
driving_force = 0.0001
```
%% Cell type:markdown id: tags:
The only parameter of the model is the so-called yield_stress. The main idea is that no strain rate is observed below some stress. However, this leads to the problem that the modified relaxation rate might no longer lead to stable LBM simulations. Thus an upper and lower limit for the shear relaxation rate must be given. All the parameters are combined in the `CassonsParameters` dataclass
%% Cell type:code id: tags:
``` python
# yield stress
sigma_y = 2*1e-6
parameters = CassonsParameters(yield_stress=sigma_y, omega_min=0.2, omega_max=1.98)
```
%% Cell type:code id: tags:
``` python
dh = ps.create_data_handling(domain_size=domain_size, periodicity=(True, False, False))
src = dh.add_array('src', values_per_cell=len(stencil))
dh.fill('src', 0.0, ghost_layers=True)
dst = dh.add_array('dst', values_per_cell=len(stencil))
dh.fill('dst', 0.0, ghost_layers=True)
velField = dh.add_array('velField', values_per_cell=dh.dim)
dh.fill('velField', 0.0, ghost_layers=True)
```
%% Cell type:markdown id: tags:
To activate the Casson model in the derivation of the LBM equations, simply pass the parameter class to the LBMConfig
%% Cell type:code id: tags:
``` python
lbm_config = LBMConfig(stencil=Stencil.D3Q27, method=Method.SRT,
relaxation_rate=1, compressible=False, force=(driving_force / L, 0,0),
cassons=parameters,
output={'velocity': velField}, kernel_type='stream_pull_collide')
method = create_lb_method(lbm_config=lbm_config)
```
%% Cell type:code id: tags:
``` python
init = pdf_initialization_assignments(method, 1.0, velocity=velField.center_vector, pdfs=src.center_vector)
ast_init = ps.create_kernel(init, target=dh.default_target)
kernel_init = ast_init.compile()
dh.run_kernel(kernel_init)
```
%% Cell type:markdown id: tags:
The main expression for the Casson model is:
$$
\lvert \dot{\gamma} \rvert = 2 \sqrt{S_{\alpha \beta} S_{\alpha \beta}} = \frac{3 \sigma}{\tau_\mu \nu^2 \rho \Delta t}
$$
where $\lvert \dot{\gamma} \rvert$ is the shear strain rate, $\sigma$ is the shear stress, $\nu$ is a constant viscosity $\rho$ is the density and $\Delta t$ is the lattice timestep size. The strain rate tensor is computed in the same way as in `Tutorial 06: Modifying a LBM method: Smagorinsky model`.
In order to calculate the adapted viscosity the following equation is used:
$$
\sqrt{\frac{\mu}{\eta}} = \frac{1}{1 - \theta} \left[1 + \sqrt{\theta \left[ 1 + \frac{\rho \Delta t \nu^2}{\eta} \frac{3}{2} \left( 1 - \theta \right) \right]} \right]
$$
where $\theta = \frac{\sigma_y}{\sigma}$
%% Cell type:code id: tags:
``` python
lbm_optimisation = LBMOptimisation(symbolic_field=src, symbolic_temporary_field=dst)
update = create_lb_update_rule(lbm_config=lbm_config,
lbm_optimisation=lbm_optimisation)
ast_kernel = ps.create_kernel(update, target=dh.default_target, cpu_openmp=False)
kernel = ast_kernel.compile()
```
%% Cell type:code id: tags:
``` python
update
```
%%%% Output: execute_result
# you can look at the complete equation set by removing the comment below
AssignmentCollection: dst_C^10, dst_C^24, dst_C^4, dst_C^26, dst_C^7, velField_C^1, dst_C^17, dst_C^6, dst_C^25, velField_C^2, dst_C^8, dst_C^19, dst_C^12, dst_C^21, dst_C^14, dst_C^18, velField_C^0, dst_C^9, dst_C^16, dst_C^3, dst_C^5, dst_C^2, dst_C^1, dst_C^11, dst_C^20, dst_C^22, dst_C^13, dst_C^15, dst_C^0, dst_C^23 <- f(src_BE^13, src_TE^17, src_T^6, src_BSE^20, src_TW^18, src_E^3, src_TNE^26, src_TSW^23, src_BW^14, src_BNE^22, src_BSW^19, src_C^0, src_N^2, src_S^1, src_TS^15, src_NE^9, src_B^5, src_SE^7, src_TN^16, src_TNW^25, src_W^4, src_SW^8, src_NW^10, src_TSE^24, src_BS^11, src_BN^12, src_BNW^21)
# update
```
%% Cell type:code id: tags:
``` python
def pipe_geometry_callback(x, y, z):
global W
radius = W / 2
y_mid = W / 2
z_mid = W / 2
return (y - y_mid) ** 2 + (z - z_mid) ** 2 > radius ** 2
```
%% Cell type:code id: tags:
``` python
bh = LatticeBoltzmannBoundaryHandling(method, dh, src.name, name="bh")
peridocity = LBMPeriodicityHandling(stencil=stencil, data_handling=dh, pdf_field_name=src.name)
wall = NoSlip("wall")
bh.set_boundary(wall, mask_callback=pipe_geometry_callback)
plt.figure(dpi=200)
plt.boundary_handling(bh, make_slice[0.5, :, :])
```
%%%% Output: display_data
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%% Cell type:code id: tags:
``` python
def timeloop(timeSteps):
for i in range(timeSteps):
bh()
peridocity()
dh.run_kernel(kernel)
dh.swap("src", "dst")
```
%% Cell type:code id: tags:
``` python
timeloop(2000)
plt.figure(dpi=200)
plt.scalar_field(dh.gather_array('velField')[domain_size[0] // 2, :, :, 0]);
plt.colorbar()
```
%%%% Output: execute_result
<matplotlib.colorbar.Colorbar at 0x130dec1f0>
<matplotlib.colorbar.Colorbar at 0x12dd99400>
%%%% Output: display_data
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%% Cell type:code id: tags:
``` python
def poiseuille_profil(r, nu, a, dpdx, dim):
dim_scale = 2 if dim == 2 else 1
return -dim_scale/(4 * nu) * (a**2 - r**2) * dpdx
def poiseuille_profil_nN(r, rc, nu, a, dpdx, dim):
dim_scale = 2 if dim == 2 else 1
if abs(r) >= rc:
p = a**2-r**2-8/3*rc**(1/2)*(a**(3/2)-abs(r)**(3/2))+2*rc*(a-abs(r))
else:
p = a**2-8/3*rc**(1/2)*a**(3/2)+2*rc*a-1/3*rc**2
return -dim_scale/(4*nu)*dpdx*p
dpdx = -driving_force / L
if stencil.D == 2:
r_c = abs(1/ math.sqrt(2)*sigma_y/dpdx)
elif stencil.D == 3:
r_c = abs(1/ math.sqrt(2)*2*sigma_y/dpdx)
analytical_solution = [poiseuille_profil(r, nu, W/2, dpdx, stencil.D) for r in range(math.ceil(-W/2), math.floor(W/2)+1)]
analytical_solution_nN = [poiseuille_profil_nN(r, r_c, nu, W/2, dpdx, stencil.D) for r in range(math.ceil(-W/2), math.floor(W/2)+1)]
```
%% Cell type:code id: tags:
``` python
plt.figure(dpi=200)
plt.scalar_field(dh.gather_array('velField')[:, domain_size[1] // 2, :, 0]);
plt.colorbar()
```
%%%% Output: execute_result
<matplotlib.colorbar.Colorbar at 0x163128160>
<matplotlib.colorbar.Colorbar at 0x12f07a610>
%%%% Output: display_data
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%% Cell type:code id: tags:
``` python
plt.plot(dh.gather_array(velField.name)[domain_size[0]//2, domain_size[1]//2, :, 0])
plt.plot(analytical_solution_nN)
plt.plot(analytical_solution)
plt.legend(["Non-Newtonian flow simulation", "Analytic non-Newtonian flow", "Analytic Newtonian flow"])
```
%%%% Output: execute_result
<matplotlib.legend.Legend at 0x1631c7fd0>
<matplotlib.legend.Legend at 0x12f026a30>
%%%% Output: display_data
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)
%% Cell type:code id: tags:
``` python
a = dh.gather_array(velField.name)[domain_size[0]//2, domain_size[1]//2, :, 0]
b = analytical_solution_nN
assert np.max((a - b) / b) < 0.07
```
......
......@@ -58,7 +58,7 @@ def add_cassons_model(collision_rule, parameter: CassonsParameters, omega_output
# rhs of equation 14 in https://doi.org/10.1007/s10955-005-8415-x
# Note that C_2 / C_4 = 3 for all configurations thus we directly insert it here
eq14 = one / (one - theta) * (one + sp.sqrt(theta * (one + rho / eta * sp.Rational(3, 2) * (one - theta))))
eq14 = one / (one - theta) * (one + sp.sqrt(theta * (one + rho / eta * sp.Rational(1, 6) * (one - theta))))
new_omega = one / tau
omega_cond = sp.Piecewise((omega_min, new_omega < omega_min), (omega_max, new_omega > omega_max), (new_omega, True))
......
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