Benchmark of different CFL conditions for IMPES

Abstract

The IMplicit Pressure Explicit Saturation (IMPES) method is a prevalent way to simulate multiphase flows in porous media. The numerical stability of this sequential method implies limitations on the time step, which may depend on the flow regime studied. In this note, three stability criteria related to the IMPES method, that differ in their construction on the observed variables, are compared on homogeneous and heterogeneous configurations for different two-phase flow regimes (viscous/capillary/gravitational). This highlights that there is no single optimal criterion always ensuring stability and efficiency. For capillary dominated flows, the Todd’s condition is the most efficient one, while the standard Coat condition should be preferred for viscous flows. When gravity effects are present, Coat’s condition must be restricted, but remains more efficient than the Todd’s condition.