If `pycuda` is installed the simulation automatically runs on GPU
%% Cell type:code id: tags:
``` python
try:
importpycuda
exceptImportError:
pycuda=None
gpu=False
target=ps.Target.CPU
print('No pycuda installed')
ifpycuda:
gpu=True
target=ps.Target.GPU
```
%% Output
No pycuda installed
%% Cell type:markdown id: tags:
The conservative Allen-Cahn model (CACM) for two-phase flow is based on the work of Fakhari et al. (2017) [Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios](http://dx.doi.org/10.1103/PhysRevE.96.053301). The model can be created for two-dimensional problems as well as three-dimensional problems, which have been described by Mitchell et al. (2018) [Development of a three-dimensional
phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios](http://dx.doi.org/10.1103/PhysRevE.96.053301). Furthermore, cascaded lattice Boltzmann methods can be combined with the model which was described in [A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast](http://dx.doi.org/10.1016/j.camwa.2019.08.018)
The CACM is suitable for simulating highly complex two phase flow problems with high-density ratios and high Reynolds numbers. In this tutorial, an overview is provided on how to derive the model with lbmpy. For this, the model is defined with two LBM populations. One for the interface tracking, which we call the phase-field LB step and one for recovering the hydrodynamic properties. The latter is called the hydrodynamic LB step.
%% Cell type:markdown id: tags:
## Geometry Setup
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 can be performed in either 2D- or 3D-space. For 2D simulations, only the D2Q9 stencil is supported. For 3D simulations, the D3Q15, D3Q19 and the D3Q27 stencil are supported. Note here that the cascaded LBM can not be derived for D3Q15 stencils.
The next step is to calculate all parameters which are needed for the simulation. In this example, a Rayleigh-Taylor instability test case is set up. The parameter calculation for this setup is already implemented in lbmpy and can be used with the dimensionless parameters which describe the problem.
This function returns a `AllenCahnParameters` class. It is struct like class holding all parameters for the conservative Allen Cahn model:
%% Cell type:code id: tags:
``` python
parameters
```
%% Output
<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x126d30cd0>
<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x10d542d00>
%% Cell type:markdown id: tags:
## Fields
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/). This object holds all fields and manages the kernel runs.
For both LB steps, a weighted orthogonal MRT (WMRT) method is used. It is also possible to change the method to a simpler SRT scheme or a more complicated CLBM scheme. The CLBM scheme can be obtained with `Method.CENTRAL_MOMENT`. Note here that the hydrodynamic LB step is formulated as an incompressible velocity-based LBM. Thus, the velocity terms can not be removed from the equilibrium in the central moment space.
For the Allen-Cahn LB step, the Allen-Cahn equation needs to be applied as a source term. Here, a simple forcing model is used which is directly applied in the moment space:
where $\phi$ is the phase-field, $\phi_0$ is the interface location, $\Delta t$ it the timestep size $\xi$ is the interface width, $\boldsymbol{c}_i$ is the discrete direction from stencil_phase and $w_i$ are the weights. Furthermore, the equilibrium needs to be shifted:
In the above equations $p^*$ is the normalised pressure which can be obtained from the zeroth order moment of the hydrodynamic distribution function $g$. The lattice speed of sound is given with $c_s$ and the chemical potential is $\mu_\phi$. Furthermore, the viscosity is $\nu$ and $\Omega$ is the moment-based collision operator. Note here that the hydrodynamic equilibrium is also adjusted as shown above for the phase-field distribution functions.
For CLBM methods the forcing is applied directly in the central moment space. This is done with the `CentralMomentMultiphaseForceModel`. Furthermore, the GUO force model is applied here to be consistent with [A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast](http://dx.doi.org/10.1016/j.camwa.2019.08.018). Here we refer to equation D.7 which can be derived for 3D stencils automatically with lbmpy.
In our framework the pull scheme is applied as streaming step. Furthermore, the update of the phase-field is directly integrated into the kernel. As a result of this, a second temporary phase-field is needed.
Here, the push scheme is applied which is easier due to the data access required for the viscous force term. Furthermore, the velocity update is directly done in the kernel.
If `pycuda` is installed the simulation automatically runs on GPU
%% Cell type:code id: tags:
``` python
try:
importpycuda
exceptImportError:
pycuda=None
gpu=False
target=ps.Target.CPU
print('No pycuda installed')
ifpycuda:
gpu=True
target=ps.Target.GPU
```
%% Output
No pycuda installed
%% Cell type:markdown id: tags:
The conservative Allen-Cahn model (CACM) for two-phase flow is based on the work of Fakhari et al. (2017) [Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios](http://dx.doi.org/10.1103/PhysRevE.96.053301). The model can be created for two-dimensional problems as well as three-dimensional problems, which have been described by Mitchell et al. (2018) [Development of a three-dimensional
phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios](http://dx.doi.org/10.1103/PhysRevE.96.053301). Furthermore, cascaded lattice Boltzmann methods can be combined with the model which was described in [A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast](http://dx.doi.org/10.1016/j.camwa.2019.08.018)
The CACM is suitable for simulating highly complex two phase flow problems with high-density ratios and high Reynolds numbers. In this tutorial, an overview is provided on how to derive the model with lbmpy. For this, the model is defined with two LBM populations. One for the interface tracking, which we call the phase-field LB step and one for recovering the hydrodynamic properties. The latter is called the hydrodynamic LB step.
%% Cell type:markdown id: tags:
## Geometry Setup
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 can be performed in either 2D- or 3D-space. For 2D simulations, only the D2Q9 stencil is supported. For 3D simulations, the D3Q15, D3Q19 and the D3Q27 stencil are supported. Note here that the cascaded LBM can not be derived for D3Q15 stencils.
The next step is to calculate all parameters which are needed for the simulation. In this example, a Rayleigh-Taylor instability test case is set up. The parameter calculation for this setup is already implemented in lbmpy and can be used with the dimensionless parameters which describe the problem.
This function returns a `AllenCahnParameters` class. It is struct like class holding all parameters for the conservative Allen Cahn model:
%% Cell type:code id: tags:
``` python
parameters
```
%% Output
<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x126d30cd0>
<lbmpy.phasefield_allen_cahn.parameter_calculation.AllenCahnParameters at 0x10d542d00>
%% Cell type:markdown id: tags:
## Fields
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/). This object holds all fields and manages the kernel runs.
For both LB steps, a weighted orthogonal MRT (WMRT) method is used. It is also possible to change the method to a simpler SRT scheme or a more complicated CLBM scheme. The CLBM scheme can be obtained with `Method.CENTRAL_MOMENT`. Note here that the hydrodynamic LB step is formulated as an incompressible velocity-based LBM. Thus, the velocity terms can not be removed from the equilibrium in the central moment space.
For the Allen-Cahn LB step, the Allen-Cahn equation needs to be applied as a source term. Here, a simple forcing model is used which is directly applied in the moment space:
where $\phi$ is the phase-field, $\phi_0$ is the interface location, $\Delta t$ it the timestep size $\xi$ is the interface width, $\boldsymbol{c}_i$ is the discrete direction from stencil_phase and $w_i$ are the weights. Furthermore, the equilibrium needs to be shifted:
In the above equations $p^*$ is the normalised pressure which can be obtained from the zeroth order moment of the hydrodynamic distribution function $g$. The lattice speed of sound is given with $c_s$ and the chemical potential is $\mu_\phi$. Furthermore, the viscosity is $\nu$ and $\Omega$ is the moment-based collision operator. Note here that the hydrodynamic equilibrium is also adjusted as shown above for the phase-field distribution functions.
For CLBM methods the forcing is applied directly in the central moment space. This is done with the `CentralMomentMultiphaseForceModel`. Furthermore, the GUO force model is applied here to be consistent with [A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast](http://dx.doi.org/10.1016/j.camwa.2019.08.018). Here we refer to equation D.7 which can be derived for 3D stencils automatically with lbmpy.
In our framework the pull scheme is applied as streaming step. Furthermore, the update of the phase-field is directly integrated into the kernel. As a result of this, a second temporary phase-field is needed.
Here, the push scheme is applied which is easier due to the data access required for the viscous force term. Furthermore, the velocity update is directly done in the kernel.
Markus Holzer authored