# Model options

In this section it is described how the input file can be configured in order to specify the settings of the problem at hand. The input file must be passed as first argument to the MFIX-Exa executable.

The following inputs must be preceded by “mfix.”

| Description | Type | Default
--- | --- | --- | ---
gravity | Gravity vector (e.g., mfix.gravity = -9.81 0.0 0.0) [required] | Reals | 0 0 0
advect_density | Switch for turning ON (1) or OFF (0) fluid density evolution | Int | 0
advect_enthalpy | Switch for turning ON (1) or OFF (0) fluid temperature evolution | Int | 0
solve_species | Switch for turning ON (1) or OFF (0) fluid species mass fraction evolution | Int | 0
constraint_type | Select which constraint to apply to the problem. Available options include: ‘incompressiblefluid’ for incompressibility constraint ‘idealgasopensystem’ for Ideal Gas-Open System constraint ‘idealgasclosedsystem’ for Ideal Gas-Closed System constraint | String | IncompressibleFluid

## Fluid discretization

The following inputs must be preceded by “mfix.”

Key | Description | Type | Default
--- | --- | --- | ---
advection_type | Predictor-Corrector Method of Lines (“mol”) or Godunov (“godunov”) | String | Godunov
redistribution_type | Use flux (“FluxRedist”), state (“StateRedist”) or no (“NoRedist”) redistribution | String | StateRedist
redistribute_before_nodal_proj | Redistribute the velocity field before the nodal projection | Bool | True
redistribute_nodal_proj | Redistribute the velocity field after the nodal projection | Bool | False
use_drag_coeff_in_proj_gp | Algebraically consistent p coeff in proj or (default) simplified form | Bool | False
use_drag_in_godunov | Include a drag term in the Godunov flux or (default) not | Bool | False
correction_small_volfrac | Threshold volume fraction for correcting small cell velocity at the end of the predictor and corrector | Real | 1.e-4

Notes: The code was originally developed with MOL and FluxRedist. Preliminary tests show that the new single-step Godunov method is roughly twice as fast as the predictor-corrector MOL at the same time step (e.g., CFL limited to 0.5). Further, the Godunov method allows for roughly twice the time step, CFL should be limited to 0.9 for stability. Finally, it is recommended that the Godunov method be used in conjunction with StateRedist. While not fully vetted, early tests also show increased stability in complex geometries for a StateRedist- Godunov scheme compared to the previous FluxRedist-MOL scheme.

## Additional constraitns

Additional constraints may be imposed on problems which are under-determined by IBCs, typically occurring in periodic domains. Currently, only particle constraints are supported. The prefix particles. should be applied to all input keywords listed below.

| Description | Type | Default
--- | --- | --- | ---
constraint | Constraint type. Available options include: ‘mean_velocity’ | String | None

For the mean_velocity constraint, the following inputs can be defined.

| Description | Type | Default
--- | --- | --- | ---
mean_velocity_x | mean particle velocity in dir=0 | Real | Undefined
mean_velocity_y | mean particle velocity in dir=1 | Real | Undefined
mean_velocity_z | mean particle velocity in dir=2 | Real | Undefined

Below is an example for zero mean particle velocity in all three directions.

    particles.constraint = "mean_velocity"

    particles.constraint.mean_velocity_x = 0.
    particles.constraint.mean_velocity_y = 0.
    particles.constraint.mean_velocity_z = 0.

## Deposition scheme

The following inputs must be preceded by “mfix.”

| Description | Type | Default
--- | --- | --- | ---
deposition_scheme | The algorithm that will be used to deposit particles quantities to the Eulerian grid. Available methods are: ‘centroid’ ‘trilinear’ ‘true-dpvm’ divided particle volume method ‘trilinear-dpvm-square’ dpvm with square filter | String | ‘trilinear’
deposition_scale_factor | The deposition scale factor. Only applies to ‘true-dpvm’ and ‘trilinear-dpvm-square’ methods. Its value must be in the interval [0, dx/2], where dx is the cell edge size. | Real | 1.0
deposition_diffusion_coeff | If a positive value is set, a diffusion equation with this diffusion coefficient is solved to smooth deposited quantities. | Real | -1.0

In the following subsections, the four possible deposition methods are briefly described and illustrated.

### Centroid

In the centroid deposition scheme, particles’ quantities are deposited only to the Eulerian grid cell to which the particle’s center belongs.

Fig. 4 Example of centroid deposition.

### Trilinear

In the trilinear deposition scheme, particles’ quantities are deposited linearly to the eight Eulerian grid cells that surround its center.

Fig. 5 Example of trilinear deposition.

### Divided Particle Volume Method (DPVM)

In the DPVM method, particles’ quantities are deposited to the Eulerian grid cells that they intersect, and the deposition weights are equal to the percentage of the particle’ volume that intersects the given cell.

Fig. 6 Example of dpvm deposition.

### Square DPVM

In the square DPVM method, particles’ quantities are deposited to the Eulerian grid similarly to the DPVM method, but with a filter applied to the deposition scheme.

Fig. 7 Example of square dpvm deposition.

The following inputs must be preceded by “mfix.”

Key | Description | Type | Default
--- | --- | --- | ---
deposition_redist_type | Redistribute excess solids using max packing (“MaxPack”) or state (“StateRedist”) algorithms. | String | MaxPack
deposition_redist_vfrac | The threshold cell volume fraction when using “StateRedist” for deposition redistribution. | Real | 0.1

## Drag models

The following inputs must be preceded by “mfix.”

| Description | Type | Default
--- | --- | --- | ---
drag_type | Which drag model to use | String | None

The options currently supported in mfix are `WenYu`, `Gidaspow`, `BVK2`, or `UserDrag`.

If one of these is not specified, the code will abort with

    amrex::Abort::0::"Don't know this drag type!!!

The drag models are defined in src/src_des/des_drag_K.H

If the user wishes to use their own drag model, they must

> - specify `mfix.drag_type = UserDrag` in the inputs file

> - provide the code in the ComputeDragUser routine in a local usr_drag.cpp file. An example can be found in tests/DEM06-x.

With the variables defined as follows:

>     EPg     - gas volume fraction
>     Mug     - gas laminar viscosity
>     ROpg    - gas density * EP_g
>     vrel    - magnitude of gas-solids relative velocity
>     DPM     - particle diameter of solids phase M
>     DPA     - average particle diameter
>     PHIS    - solids volume fraction of solids phases
>     fvelx   - x component of the fluid velocity at the particle position
>     fvely   - y component of the fluid velocity at the particle position
>     fvelz   - z component of the fluid velocity at the particle position
>     i, j, k - particle cell indices
>     pid     - particle id number

The `WenYu` model is defined as

>      RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

>     if (RE <= 1000.0)
>     {
>         C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
>     }
>     else
>     {
>         C_d = 0.44;
>     }

>     if (RE < DEMParams::eps) return 0.0;
>     return 0.75 * C_d * vrel * ROPg * std::pow(EPg, -2.65) / DPM;

The `Gidaspow` model is defined as

>     ROg = ROPg / EPg;

>     RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

>     // Dense phase - EPg <= 0.8
>     Ergun = 150.0*(1.0 - EPg)*Mug / (EPg*DPM*DPM) + 1.75*ROg*vrel/DPM;

>     // Dilute phase - EPg > 0.8
>     if (RE <= 1000.0)
>     {
>         C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
>     }
>     else
>     {
>         C_d = 0.44;
>     }

>     WenYu = 0.75*C_d*vrel*ROPg*std::pow(EPg, -2.65) / DPM;

>     // switch function
>     PHI_gs = atan(150.0*1.75*(EPg - 0.8))/M_PI / DPM;

>     // blend the models
>     if (RE < DEMParams::eps) return 0.0;
>     return (1.0 - PHI_gs)*Ergun + PHI_gs*WenYu;

The `BVK2` model is defined as

>     amrex::Real RE = (Mug > 0.0) ? DPA*vrel*ROPg/Mug : DEMParams::large_number;

>     if (RE > DEMParams::eps)
>     {
>         oEPgfour = 1.0 / EPg / EPg / EPg / EPg;

>         // eq(9) BVK J. fluid. Mech. 528, 2005
>         // (this F_Stokes is /= of Koch_Hill by a factor of ep_g)
>         F_Stokes = 18.0*Mug*EPg/DPM/DPM;

>         F = 10.0*PHIS/EPg/EPg + EPg*EPg*(1.0 + 1.5*sqrt(PHIS));

>         F += RE*(0.11*PHIS*(1.0+PHIS) - 4.56e-3*oEPgfour +
>              std::pow(RE, -0.343)*(0.169*EPg + 6.44e-2*oEPgfour));

>         // F += 0.413*RE/(24.0*EPg*EPg) *
>         //     (1.0/EPg + 3.0*EPg*PHIS + 8.4/std::pow(RE, 0.343)) /
>         //     (1.0 + std::pow(10.0, 3.0*PHIS)/std::pow(RE, 0.5 + 2.0*PHIS));

>         return F*F_Stokes;
>     }
>     else
>     {
>         return 0.0;
>     }

## Heat transfer coefficients

The following inputs must be preceded by “mfix.”

| Description | Type | Default
--- | --- | --- | ---
convection_type | Which HTC model to use | String | RanzMarshall

The options currently supported in mfix are `RanzMarshall` (default) and `Gunn`. In both models the HTC is determined from a Nusslet number corelation.

The RanzMarshall Nusselt number correlation is defined as:

>     amrex::Real N_Nu = 2.0 + 0.6 * std::sqrt(N_Re) * std::pow(N_Pr, 0.333);

The Gunn Nusselt number correlation is defined as:

>     amrex::Real N_Nu =
>         (7 - 10*EPg + 5*EPg*EPg)*(1 + .7*std::pow(N_Re, 0.2)*std::cbrt(N_Pr))
>         + (1.33 - 2.4*EPg + 1.2*EPg*EPg)*std::pow(N_Re, 0.7)*std::cbrt(N_Pr);