A stable pressure-correction MAC scheme for the fluid-Poroelastic material interaction problem

Abstract

In this paper, we propose and analyse pressure-correction schemes based on marker and cell (MAC) method for the linear Stokes–Biot system with a fixed interface. The implicit backward Euler scheme for the time discretization is used, whereas the coupling terms are treated explicitly. These schemes are computationally efficient in that we only solve two decoupled problems. And for Stokes equations, we solve one vector-valued elliptic equation and one scalar-value Poisson equation per time step. These methods have optimal order without the incompressibility constraint of the Stokes system. We prove rigorously that they are unconditionally stable and present the numerical experiments to show their performance.