A second order partitioned method with grad-div stabilization for the non-stationary dual-porosity-Stokes model

Abstract

This paper proposes, analyzes and tests a second-order time-accurate partitioned method for the coupling dual-porosity-Stokes equations. The algorithm combines a backward differentiation formula and the explicit second order's extrapolation method, and decouples the coupled problem to three sub-domain equations (matrix pressure equation, microfracture pressure equation and Stokes equation) at each time step. To improve the accuracy of the approximate solutions and enhance conservation of mass, the algorithm adds a grad-div stabilization term to the partitioned code and extends it to modular grad-div algorithm. We derive the time stability of the algorithm without the time step restriction and error estimate for fully discretized schemes using finite element spatial discretization. Numerical experiments validate the accuracy and advantage of grad-div stabilization algorithms and support the theoretical analysis.