Test-case for the mean drag force in a simple cubic array at Stokes flow and at
moderate Reynolds numbers. Simulation results compared to Zick and Homsy (1982)
(Stokes flow) and Hill et all (2001), Tenneti et al (2011), and Das et al (2016)
(moderate Re-flow). 

Running the simulation:

- To run the simulation:
  ./Allrun.sh

- To clean-up the directory after the simulation is run: 
  ./Allclean.sh 

- Simulation parameters are summarized in ./settings

- To enable automatic post-processing (graph plotting), set "runVerification=true" 
  (and "testStokes=true" for testing Stokes flow) in ./Allrun.sh (works with 
  Python 3.11.5)

- Assembly generation parameters are set in ./system/searchableSurfacesDict

- "sphereList" (list of searchable surfaces) and "eMeshesList" (list of eMeshes)
  is included in ./system/snappyHexMeshDict

- "includeForcesFiles" (list of force function objects for post-processing) is
  included in ./system/controlDict


To run with patchMeanVelocityForce: 

 cp ./patchMeanVeloctyForce/system/fvOptions  ./system/
 cp ./patchMeanVeloctyForce/system/searchableSurfacesDict  ./system/
 cp ./patchMeanVeloctyForce/0.orig/p ./0.orig/
 
References: 
    Hill et all (2001)
       R. J. Hill, D. L. Koch, and A. J. C. Ladd, "Moderate-Reynolds-number 
       flows in ordered and random arrays of spheres," Journal of Fluid 
       Mechanics, vol. 448, pp. 243-278, 2001.

    Tenneti et al (2011)
       S. Tenneti, R. Garg, and S. Subramaniam, "Drag law for monodisperse 
       gas-solid systems using particle-resolved direct numerical simulation of 
       flow past fixed assemblies of spheres, "International Journal of 
       Multiphase Flow, vol. 37, pp. 1072-1092, 2011.

    Das et al (2016)
       S. Das, N. G. Deen, and J. A. M. Kuipers, "Immersed boundary method (IBM)
       based direct numerical simulation of open-cell solid foams: 
       Hydrodynamics," AIChE Journal, vol. 63, pp. 1152-1173, 2016.

    Zick and Homsy (1982)
       A. A. Zick and G. M. Homsy, "Stokes flow through periodic array of 
       spheres," Journal of Fluid Mechanics, vol. 115, pp. 13-26, 1982.
