Ghost or Wall Particles

One of the first approaches employed to impose a non-slip boundary condition at an external wall or at a moving object in a MFC solvent was to use ghost or wall particles [36,81]. In other mesoscale methods such as LB, no-slip conditions are modeled using the bounce-back rule the velocity of the particle is inverted from v to -V when it intersects a wall. For planar walls which coincide with the boundaries of the collision cells, the same procedure can be used in MFC. However, the walls will generally not coincide with, or even be parallel to, the cell walls. Furthermore, for small mean free paths, where a shift of the cell lattice is required to guarantee Galilean invariance, partially occupied boundary cells are unavoidable, even in the simplest flow geometries. 

The simple bounce-back rule fails to guarantee no-slip boundary conditions in the case of partially filled cells. The following generalization of the bounce-back rule has therefore been suggested. For all cells that are cut by walls, fill the wall part of the cell with a sufficient number of virtual particles in order to make the total number of particles equal to M, the average number of particles per cell. The velocities of the wall particles are drawn from a Maxwell-Boltzmann distribution with zero mean 

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