The finite difference reservoir flow simulator for a single phase is a straightforward explicit finite difference implementation of the corresponding fluid flow equation 8:
where is the transmissibility. Each grid point represents a homogeneous subsurface cell. A straightforward stability analysis (see the finite difference wave equation section) yields and . Figure 1 shows snapshots of a reservoir of constant transmissibility and random sources of pressure. The pressure impulses diffuse over time as we would expect from a solution to a parabolic differential equation.