The locking-free finite difference method based on staggered grids for the coupled Stokes–Biot problem

Abstract

The finite difference method on staggered grids is developed to solve the coupled Stokes–Biot problem using the covolume integration on the interface. We construct the finite difference scheme on staggered grids, and analyse the stability and optimal-order error estimates. The theoretical results hold uniformly about the Lam constant indicating incompressibility of a deformable porous medium and the storage coefficient , which indicates our method is locking-free. Some numerical tests are given to verify the analysis of convergence, which supports the theoretical results. In addition, the numerical examples show the strong mass conservation and the robustness of the model with respect to its parameters.