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James McClure
2021-10-21 20:24:10 -04:00
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76
docs/source/userGuide/models/color/protocols/centrifuge.rst
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@@ -30,14 +30,76 @@ This is because a positive body force will favor a larger saturation of fluid A
(positive capillary pressure ) whereas a negative body force will favor a lower
saturation of fluid A (negative capillary pressure).
The simplest way to infer the capillary pressure is based on consideration of the average
fluid pressures, which are logged to the output files ``timelog.csv`` and ``subphase.csv``.
In the units of the lattice Boltzmann simulation, the interfacial tension is given
as :math:`\gamma_{wn} = 6 \alpha`. Suppose that the physical interfacial tension is given by
:math:`\gamma_{wn}^\prime`, provided in units of Pa-m. The capillary pressure in pascal will
then be given by
To enable the ``centrifuge`` protocol such that the pressure of fluid B is higher than
fluid A, the following keys can be set. Increasing the body force will lead to a larger
capillary pressure
.. math::
:nowrap:
$$
p_c^\prime = \frac{\gamma_{wn}^\prime (p_n - p_w)}{\gamma_{wn} \Delta x}
$$
where :math:`\Delta x` is the voxel length in meters.
To enable the ``centrifuge`` protocol such that the effective pressure of fluid B is higher
than fluid A, the input file can be specified as below. Increasing the body force will lead to
a larger capillary pressure.
.. code-block:: c
Color {
protocol = "centrifuge"
timestepMax = 1000000 // maximum timtestep
alpha = 0.005 // controls interfacial tension
rhoA = 1.0 // controls the density of fluid A
rhoB = 1.0 // controls the density of fluid B
tauA = 0.7 // controls the viscosity of fluid A
tauB = 0.7 // controls the viscosity of fluid B
F = 0, 0, -1.0e-5 // body force
din = 1.0 // inlet density (controls pressure)
dout = 1.0 // outlet density (controls pressure)
WettingConvention = "SCAL" // convention for sign of wetting affinity
ComponentLabels = 0, -1, -2 // image labels for solid voxels
ComponentAffinity = 1.0, 1.0, 0.6 // controls the wetting affinity for each label
Restart = false
}
Domain {
Filename = "Bentheimer_LB_sim_intermediate_oil_wet_Sw_0p37.raw"
ReadType = "8bit" // data type
N = 900, 900, 1600 // size of original image
nproc = 2, 2, 2 // process grid
n = 200, 200, 200 // sub-domain size
offset = 300, 300, 300 // offset to read sub-domain
voxel_length = 1.66 // voxel length (in microns)
ReadValues = -2, -1, 0, 1, 2 // labels within the original image
WriteValues = -2, -1, 0, 1, 2 // associated labels to be used by LBPM
BC = 3 // boundary condition type (0 for periodic)
}
Analysis {
analysis_interval = 1000 // logging interval for timelog.csv
subphase_analysis_interval = 5000 // loggging interval for subphase.csv
visualization_interval = 100000 // interval to write visualization files
N_threads = 4 // number of analysis threads (GPU version only)
restart_interval = 1000000 // interval to write restart file
restart_file = "Restart" // base name of restart file
}
Visualization {
write_silo = true // write SILO databases with assigned variables
save_8bit_raw = true // write labeled 8-bit binary files with phase assignments
save_phase_field = true // save phase field within SILO database
save_pressure = false // save pressure field within SILO database
save_velocity = false // save velocity field within SILO database
}
FlowAdaptor {
}
.. code-block:: bash
protocol = "centrifuge"
F = 0, 0, -1.0e-5

48
docs/source/userGuide/models/color/protocols/coreFlooding.rst
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@@ -33,7 +33,7 @@ The volumetric flow rate is related to the fluid velocity based on
where :math:`C_{xy}` is the cross-sectional area and :math:`\epsilon`
is the porosity. Given a particular experimental system
self-similar conditions can be determined for the lattice Boltzmann
simulation by matching the non-dimensional :math:`mbox{Ca}`. It is nearly
simulation by matching the non-dimensional :math:`\mbox{Ca}`. It is nearly
awlays advantageous for the timestep to be as large as possible so
that time-to-solution will be more favorable. This is accomplished by
@@ -59,5 +59,51 @@ will necessarily restrict the LB parameters that can be used, which are ultimate
manifested as a constraint on the size of a timestep.
.. code-block:: c
Color {
protocol = "core flooding"
capillary_number = 1e-4 // capillary number for the displacement
timestepMax = 1000000 // maximum timtestep
alpha = 0.005 // controls interfacial tension
rhoA = 1.0 // controls the density of fluid A
rhoB = 1.0 // controls the density of fluid B
tauA = 0.7 // controls the viscosity of fluid A
tauB = 0.7 // controls the viscosity of fluid B
F = 0, 0, 0 // body force
WettingConvention = "SCAL" // convention for sign of wetting affinity
ComponentLabels = 0, -1, -2 // image labels for solid voxels
ComponentAffinity = 1.0, 1.0, 0.6 // controls the wetting affinity for each label
Restart = false
}
Domain {
Filename = "Bentheimer_LB_sim_intermediate_oil_wet_Sw_0p37.raw"
ReadType = "8bit" // data type
N = 900, 900, 1600 // size of original image
nproc = 2, 2, 2 // process grid
n = 200, 200, 200 // sub-domain size
offset = 300, 300, 300 // offset to read sub-domain
voxel_length = 1.66 // voxel length (in microns)
ReadValues = -2, -1, 0, 1, 2 // labels within the original image
WriteValues = -2, -1, 0, 1, 2 // associated labels to be used by LBPM
BC = 4 // boundary condition type (0 for periodic)
}
Analysis {
analysis_interval = 1000 // logging interval for timelog.csv
subphase_analysis_interval = 5000 // loggging interval for subphase.csv
visualization_interval = 100000 // interval to write visualization files
N_threads = 4 // number of analysis threads (GPU version only)
restart_interval = 1000000 // interval to write restart file
restart_file = "Restart" // base name of restart file
}
Visualization {
write_silo = true // write SILO databases with assigned variables
save_8bit_raw = true // write labeled 8-bit binary files with phase assignments
save_phase_field = true // save phase field within SILO database
save_pressure = false // save pressure field within SILO database
save_velocity = false // save velocity field within SILO database
}
FlowAdaptor {
}

108
docs/source/userGuide/models/color/protocols/fractionalFlow.rst
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@@ -6,12 +6,110 @@ The fractional flow protocol is designed to perform steady-state relative
permeability simulations by using an internal routine to change the fluid
saturation by adding and subtracting mass to the fluid phases. The
mass density is updated for each fluid based on the locations where
the local rate of flow is high.
the local rate of flow is high.
.. code-block:: bash
Enabling the fractional flow protocol will automatically set the following default settings:
protocol = "fractional flow"
* ``fractional_flow_increment = 0.05`` - target change in saturation between steady points
* ``endpoint_threshold = 0.1`` - termination criterion based on the relative flow rates of fluids
* ``mass_fraction_factor = 0.006`` - percentage change to the mass fraction (per iteration)
* ``fractional_flow_epsilon = 5.0e-6`` - control the threshold velocity :math:`U_\epsilon`
* ``skip_timesteps = 50000`` - timesteps to spend in adaptive part of algorithm
* ``min_steady_timesteps = 1000000`` - minimum number of timesteps per steady point
* ``max_steady_timesteps = 1000000`` - maximum number of timesteps per steady point
Any of these values can be manually overriden by setting the appropriate key to a custom value
within the ``FlowAdaptor`` section of the input file database. The fractional flow
will enforce periodic boundary conditions ``BC = 0``, and is not compatible with other
boundary condition routines. A warning message will be printed if ``BC`` is set to a value
other than ``0``.
The basic idea for the fractional flow algorithm is to define an algorithm to modify the
fluid saturation that will:
(1) minimize the introduction of end effects and gradients in saturation
(2) respect the structure and connectivity of the fluid phases to the maximum extent
(3) minimize the transient disruption to the flow behavior so that fewer timesteps are required to reach steady
state
The strategy used to accomplish these objectives is to change saturation by either increasing
or decreasing the mass within each fluid, depending on the sign of ``mass_fraction_factor``.
If ``mass_fraction_factor`` is positive, the algorithm will remove mass from fluid A and add
mass to fluid B. The opposite will happen if ``mass_fraction_factor`` is negative. The algorithm
will selectively add mass to voxels where the local flow rate is high, since these will generally
correspond to the mobile (i.e. not disconnected) fluid regions. A local weighting function is determined
from the velocity :math:`\mathbf{u}_i`
.. math::
:nowrap:
$$
W_i = \frac{ U_\epsilon + |\mathbf{u}_i|}{U_\epsilon + \max{|\mathbf{u}_i|}}
$$
where :math:`\max{|\mathbf{u}_i|}` is the maximum flow speed within fluid :math:`i` and
:math:`U_\epsilon` is a threshold speed that is set to minimize the influence of spurious
currents on the mass seeding algorithm. The sum of the weighting function is used to normalize
the local weights so that the added mass will match the value specified by ``mass_fraction_factor``.
If the flow is slower than :math:`\epsilon_m`, the algorithm will tend to add mass evenly to the system.
For example, if the water is only present in films that flow very slowly, then mass will
be evenly seeded throughout entire water film. Alternatively, if one or both fluids
flows through distinct channels, the mass will be disproportionately added to these
channels where the rate of flow is high. As system relaxes, the mass will redistribute
spatially, causing a change to the fluid saturation.
.. code-block:: c
Color {
protocol = "fractional flow"
capillary_number = 1e-4 // capillary number for the displacement
timestepMax = 1000000 // maximum timtestep
alpha = 0.005 // controls interfacial tension
rhoA = 1.0 // controls the density of fluid A
rhoB = 1.0 // controls the density of fluid B
tauA = 0.7 // controls the viscosity of fluid A
tauB = 0.7 // controls the viscosity of fluid B
F = 0, 0, 1.0e-5 // body force
WettingConvention = "SCAL" // convention for sign of wetting affinity
ComponentLabels = 0, -1, -2 // image labels for solid voxels
ComponentAffinity = 1.0, 1.0, 0.6 // controls the wetting affinity for each label
Restart = false
}
Domain {
Filename = "Bentheimer_LB_RelPerm_intermediate_oil_wet_Sw_0p37.raw"
ReadType = "8bit" // data type
N = 900, 900, 1600 // size of original image
nproc = 2, 2, 2 // process grid
n = 200, 200, 200 // sub-domain size
offset = 300, 300, 300 // offset to read sub-domain
InletLayers = 0, 0, 6 // number of mixing layers at the inlet
OutletLayers = 0, 0, 6 // number of mixing layers at the outlet
voxel_length = 1.66 // voxel length (in microns)
ReadValues = -2, -1, 0, 1, 2 // labels within the original image
WriteValues = -2, -1, 0, 1, 2 // associated labels to be used by LBPM
BC = 0 // boundary condition type (0 for periodic)
}
Analysis {
analysis_interval = 1000 // logging interval for timelog.csv
subphase_analysis_interval = 5000 // loggging interval for subphase.csv
visualization_interval = 100000 // interval to write visualization files
N_threads = 4 // number of analysis threads (GPU version only)
restart_interval = 1000000 // interval to write restart file
restart_file = "Restart" // base name of restart file
}
Visualization {
write_silo = true // write SILO databases with assigned variables
save_8bit_raw = true // write labeled 8-bit binary files with phase assignments
save_phase_field = true // save phase field within SILO database
save_pressure = false // save pressure field within SILO database
save_velocity = false // save velocity field within SILO database
}
FlowAdaptor {
min_steady_timesteps = 100000 // minimum number of timesteps per steady point
max_steady_timesteps = 250000 // maximum number of timesteps per steady point
mass_fraction_factor = 0.006 // controls the rate of mass seeding in adaptive step
fractional_flow_increment = 0.05 // saturation change after each steady point
endpoint_threshold = 0.1 // endpoint exit criterion (based on flow rates)
}

52
docs/source/userGuide/models/color/protocols/imageSequence.rst
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@@ -21,7 +21,53 @@ To enable the image sequence protocol, the following keys should be set
within the ``Color`` section of the input database
.. code-block:: bash
Color {
protocol = "image sequence"
image_sequence = "Bentheimer_LB_RelPerm_intermediate_oil_wet_Sw_0p37.raw", "Bentheimer_LB_RelPerm_intermediate_oil_wet_Sw_0p72.raw"
// comma separated list of image names
capillary_number = 1e-4 // capillary number for the displacement
timestepMax = 1000000 // maximum timtestep
alpha = 0.005 // controls interfacial tension
rhoA = 1.0 // controls the density of fluid A
rhoB = 1.0 // controls the density of fluid B
tauA = 0.7 // controls the viscosity of fluid A
tauB = 0.7 // controls the viscosity of fluid B
F = 0, 0, 0 // body force
WettingConvention = "SCAL" // convention for sign of wetting affinity
ComponentLabels = 0, -1, -2 // image labels for solid voxels
ComponentAffinity = 1.0, 1.0, 0.6 // controls the wetting affinity for each label
Restart = false
}
Domain {
Filename = "Bentheimer_LB_RelPerm_intermediate_oil_wet_Sw_0p37.raw"
ReadType = "8bit" // data type
N = 900, 900, 1600 // size of original image
nproc = 2, 2, 2 // process grid
n = 200, 200, 200 // sub-domain size
offset = 300, 300, 300 // offset to read sub-domain
voxel_length = 1.66 // voxel length (in microns)
ReadValues = -2, -1, 0, 1, 2 // labels within the original image
WriteValues = -2, -1, 0, 1, 2 // associated labels to be used by LBPM
BC = 0 // boundary condition type (0 for periodic)
}
Analysis {
analysis_interval = 1000 // logging interval for timelog.csv
subphase_analysis_interval = 5000 // loggging interval for subphase.csv
visualization_interval = 100000 // interval to write visualization files
N_threads = 4 // number of analysis threads (GPU version only)
restart_interval = 1000000 // interval to write restart file
restart_file = "Restart" // base name of restart file
}
Visualization {
write_silo = true // write SILO databases with assigned variables
save_8bit_raw = true // write labeled 8-bit binary files with phase assignments
save_phase_field = true // save phase field within SILO database
save_pressure = false // save pressure field within SILO database
save_velocity = false // save velocity field within SILO database
}
FlowAdaptor {
min_steady_timesteps = 100000 // minimum number of timesteps per steady point
max_steady_timesteps = 250000 // maximum number of timesteps per steady point
}
protocol = "image sequence"
image_sequence = "image1.raw", "image2.raw"

50
docs/source/userGuide/models/color/protocols/shellAggregation.rst
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@@ -16,3 +16,53 @@ protocol is described by Wang et al. ( https://doi.org/10.1016/j.jcp.2019.108966
.. code-block:: c
Color {
protocol = "shell aggregation"
capillary_number = 1e-4 // capillary number for the displacement
timestepMax = 1000000 // maximum timtestep
alpha = 0.005 // controls interfacial tension
rhoA = 1.0 // controls the density of fluid A
rhoB = 1.0 // controls the density of fluid B
tauA = 0.7 // controls the viscosity of fluid A
tauB = 0.7 // controls the viscosity of fluid B
F = 0, 0, 0 // body force
WettingConvention = "SCAL" // convention for sign of wetting affinity
ComponentLabels = 0, -1, -2 // image labels for solid voxels
ComponentAffinity = 1.0, 1.0, 0.6 // controls the wetting affinity for each label
Restart = false
}
Domain {
Filename = "Bentheimer_LB_sim_intermediate_oil_wet_Sw_0p37.raw"
ReadType = "8bit" // data type
N = 900, 900, 1600 // size of original image
nproc = 2, 2, 2 // process grid
n = 200, 200, 200 // sub-domain size
offset = 300, 300, 300 // offset to read sub-domain
InletLayers = 0, 0, 6 // number of mixing layers at the inlet
OutletLayers = 0, 0, 6 // number of mixing layers at the outlet
voxel_length = 1.66 // voxel length (in microns)
ReadValues = -2, -1, 0, 1, 2 // labels within the original image
WriteValues = -2, -1, 0, 1, 2 // associated labels to be used by LBPM
BC = 0 // boundary condition type (0 for periodic)
}
Analysis {
analysis_interval = 1000 // logging interval for timelog.csv
subphase_analysis_interval = 5000 // loggging interval for subphase.csv
visualization_interval = 100000 // interval to write visualization files
N_threads = 4 // number of analysis threads (GPU version only)
restart_interval = 1000000 // interval to write restart file
restart_file = "Restart" // base name of restart file
}
Visualization {
write_silo = true // write SILO databases with assigned variables
save_8bit_raw = true // write labeled 8-bit binary files with phase assignments
save_phase_field = true // save phase field within SILO database
save_pressure = false // save pressure field within SILO database
save_velocity = false // save velocity field within SILO database
}
FlowAdaptor {
}

267
docs/source/userGuide/models/greyscaleColor/greyscaleColor.rst
View File

@@ -1,5 +1,5 @@
=============================================
Greyscale color model
Greyscale Color Model
=============================================
The LBPM greyscale lattice Boltzmann model is constructed to approximate the
@@ -8,6 +8,155 @@ solution in open regions. A simple constitutive form is used to model the relati
permeability in the grey regions,
***************************
Parameters
***************************
The essential model parameters for the color model are
- ``alpha`` -- control the interfacial tension between fluids -- :math:`0 < \alpha < 0.01`
- ``beta`` -- control the width of the interface -- :math:`\beta < 1`
- ``tauA`` -- control the viscosity of fluid A -- :math:`0.7 < \tau_A < 1.5`
- ``tauB`` -- control the viscosity of fluid B -- :math:`0.7 < \tau_B < 1.5`
- ``rhoA`` -- control the viscosity of fluid A -- :math:`0.05 < \rho_A < 1.0`
- ``rhoB`` -- control the viscosity of fluid B -- :math:`0.05 < \rho_B < 1.0`
- ``greyscale_endpoint_A`` -- control the endpoint for greyscale components -- :math:`S_b^{r,a}`
- ``greyscale_endpoint_B`` -- control the endpoint for greyscale components -- :math:`S_b^{r,b}`
****************************
Formulation
****************************
The greyscale color model extends the conventional two-fluid color model such that flow through
micro-porous "grey" voxels can also be treated. Extensions to the formulation are made to:
(1) implement momentum transport behavior consistent with the single phase greyscale model
(2) adapt the re-coloring term to allow for transport through microporosity.
Mass transport LBEs are constructed to model the behavior for each fluid. Within the open pore
regions, mass transport LBEs recover the behavior of the standard two-fluid color model.
Within grey voxels the standard recoloring term is disabled so that the mass transport behavior
can be described by a different rule within the microporous regions. The endpoints are
specified based on the saturation of fluid B at which fluid A ceases to percolate, :math:`S_b^{r,a}`
and the saturation of fluid B at which fluid B ceases to percolate, :math:`S_b^{r,b}`.
The endpoints should be independently specified for each class of microporosity that is labeled
in the input image. Between the endpoint values, the effective permeability is paramaterized based on the value
.. math::
:nowrap:
$$
S_{ab} = \frac{S_b - S_b^{r,b}}{S_b^{r,a} - S_b^{r,b}}
$$
At the endpoints, the effective permeability is provided as an input parameter for
each fluid. When :math:`S_b=S_b^{r,b}` the effective permeability of fluid B is
zero and :math:`K_a=K^{r,a}`. Between the endpoints the Corey model predicts the
effective permeability for fluid A according to
.. math::
:nowrap:
$$
K_a = K^{r,a} (1-S_{ab})^{\lambda^a}
$$
where :math:`\lambda^a=2` is the Corey exponent. Likewise,
When :math:`S_b=S_b^{r,a}` the effective permeability for fluid A will be zero,
and :math:`K_b=K^{r,b}` with
.. math::
:nowrap:
$$
K_b = K^{r,b} S_{ab}^{\lambda^b}
$$
Two LBEs are constructed to model the mass transport,
.. math::
:nowrap:
$$
A_q(\bm{x} + \bm{\xi}_q \delta t, t+\delta t) = w_q N_a \Big[1 + \frac{\bm{u} \cdot \bm{\xi}_q}{c_s^2}
+ \beta \frac{N_b}{N_a+N_b} \bm{n} \cdot \bm{\xi}_q\Big] \;
$$
.. math::
:nowrap:
$$
B_q(\bm{x} + \bm{\xi}_q \delta t, t+\delta t) =
w_q N_b \Big[1 + \frac{\bm{u} \cdot \bm{\xi}_q}{c_s^2}
- \beta \frac{N_a}{N_a+N_b} \bm{n} \cdot \bm{\xi}_q\Big]\;,
$$
The number density for each fluid is obtained from the sum of the mass transport distributions
.. math::
:nowrap:
$$
N_a = \sum_q A_q\;, \quad N_b = \sum_q B_q\;
$$
The phase indicator field is then defined as
.. math::
:nowrap:
$$
\phi = \frac{N_a-N_b}{N_a+N_b}
$$
The recoloring step incorporates the standard color model
rule to model anti-diffusion at the interface within the open pores. Within grey regions,
the anti-diffusion term must be disabled, since within grey voxels the length scale for fluid features
is smaller than the interface width produced from the color model. Within grey voxels the
two fluids are permitted to freely mix between the endpoints. Beyond the endpoints, the recoloring
term is used to drive spontaneous imbibition into the grey voxels
..math::
:nowrap:
$$
R_c =
$$
The fluid density and kinematic viscosity are determined based on linear interpolation
.. math::
:nowrap:
$$
\rho_0 = \frac{(1+\phi) \rho_n}{2}+ \frac{(1-\phi) \rho_w}{2} \;,
$$
.. math::
:nowrap:
$$
s_\nu = \frac{(1+\phi)}{2\tau_n} +\frac{(1-\phi)}{2\tau_w} \;,
$$
where
.. math::
:nowrap:
$$
\nu_w = \frac{1}{3}\Big(\tau_w - \frac{1}{2} \Big) \;, \quad
\nu_n = \frac{1}{3}\Big(\tau_n - \frac{1}{2} \Big) \;.
$$
These values are then used to model the momentum transport.
A D3Q19 LBE is constructed to describe the momentum transport
@@ -63,3 +212,119 @@ Combining the previous expressions,
$$
Where :math:`\bm{F}` is an external body force and :math:`c_s^2 = 1/3` is the speed of sound for the LB model.
The moments are linearly indepdendent:
.. math::
:nowrap:
$$
m_k = \sum_{q=0}^{18} M_{qk} f_q\;.
$$
The relaxation parameters are determined from the relaxation time:
.. math::
:nowrap:
$$
\lambda_1 = \lambda_2= \lambda_9 = \lambda_{10}= \lambda_{11}= \lambda_{12}= \lambda_{13}= \lambda_{14}= \lambda_{15} = s_\nu \;,
$$
.. math::
:nowrap:
$$
\lambda_{4}= \lambda_{6}= \lambda_{8} = \lambda_{16} = \lambda_{17} = \lambda_{18}= \frac{8(2-s_\nu)}{8-s_\nu} \;,
$$
The non-zero equilibrium moments are defined as
.. math::
:nowrap:
$$
m_1^{eq} = (j_x^2+j_y^2+j_z^2) - \alpha |\textbf{C}|, \\
$$
.. math::
:nowrap:
$$
m_9^{eq} = (2j_x^2-j_y^2-j_z^2)+ \alpha \frac{|\textbf{C}|}{2}(2n_x^2-n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{11}^{eq} = (j_y^2-j_z^2) + \alpha \frac{|\textbf{C}|}{2}(n_y^2-n_z^2), \\
$$
.. math::
:nowrap:
$$
m_{13}^{eq} = j_x j_y + \alpha \frac{|\textbf{C}|}{2} n_x n_y\;, \\
$$
.. math::
:nowrap:
$$
m_{14}^{eq} = j_y j_z + \alpha \frac{|\textbf{C}|}{2} n_y n_z\;, \\
$$
.. math::
:nowrap:
$$
m_{15}^{eq} = j_x j_z + \alpha \frac{|\textbf{C}|}{2} n_x n_z\;,
$$
where the color gradient is determined from the phase indicator field
.. math::
:nowrap:
$$
\textbf{C}=\nabla \phi\;.
$$
and the unit normal vector is
.. math::
:nowrap:
$$
\bm{n} = \frac{\textbf{C}}{|\textbf{C}|}\;.
$$
****************************
Boundary Conditions
****************************
Due to the nature of the contribution of the porosity to the pressure term in the Chapman-Enskog
expansion, periodic boundary conditions are recommended for ``lbpm_greyscaleColor_simulator``
and can be set by setting the ``BC`` key values in the ``Domain`` section of the
input file database
- ``BC = 0`` -- fully periodic boundary conditions
For ``BC = 0`` any mass that exits on one side of the domain will re-enter at the other
side. If the pore-structure for the image is tight, the mismatch between the inlet and
outlet can artificially reduce the permeability of the sample due to the blockage of
flow pathways at the boundary. LBPM includes an internal utility that will reduce the impact
of the boundary mismatch by eroding the solid labels within the inlet and outlet layers
(https://doi.org/10.1007/s10596-020-10028-9) to create a mixing layer.
The number mixing layers to use can be set using the key values in the ``Domain`` section
of the input database
- ``InletLayers = 5`` -- set the number of mixing layers to ``5`` voxels at the inlet
- ``OUtletLayers = 5`` -- set the number of mixing layers to ``5`` voxels at the outlet