On an optimal number of time steps for a sequential solution of an elliptic–hyperbolic system
Abstract: We consider a sequential approach for the solution of an elliptic–hyperbolic system of partial differential equations, which models a flow of two incompressible phases in porous media. The elliptic equation describes the pressure distribution in the domain, and the hyperbolic equation is the mass conservation equation for one of the phases. We propose to estimate an optimal number of the pressure updates using an analytical solution to a special 1D initial boundary value problem (IBVP) for the coupled system. We provide two procedures aimed at the estimation of an optimal set of time steps, and show that the resulting distribution of time steps yields better results than using equidistant time steps. We also show that the degree of coupling of the 1D IBVP can be quantitatively estimated using a normalized difference of the exact solution and its sequential approximation with a single time step.