As our first system, we consider the motion of a fluid through a fixed random assembly of particles. Our mental picture is that the particle assembly is a model for a random porous medium with very high porosity. In the simulation, we then have to keep the particles pinned to their initial positions. However, we calculate all forces acting between particles and liquid, but we only update the liquid's degrees of freedom in the computational timestep. Excluded volume effects due the presence of the particle phase and local frictional drag still influence the fluid motion.
Gravity is set to zero, or equivalently the flow is considered to lie in the horizontal plane.
In x direction the system has the width and boundary conditions are periodic. A typical arrangement of particles in a small system of and at and the resulting stationary flow pattern is displayed in Fig. 1 . The circles indicate the particles, the arrows direction and magnitude of the liquid flux obtained by multiplying the local liquid volume fraction with the flow velocity. We see how the particle volume fraction influences the flow pattern such that the current concentrates in regions with few particles present. Note that the fluid velocity is defined everywhere in space, even at points covered by particles and that the flow velocities should therefore be considered as average values over the specific grid cell.