An improved partitioned time stepping method based on modified characteristic FEM for the evolutionary dual-porosity-Navier–Stokes model

Abstract

In this paper, we study an improved partitioned time stepping method based on the modified characteristic finite element method for the evolutionary dual-porosity-Navier–Stokes coupling model with the Beavers–Joseph interface condition. By referring to the idea of partitioned time stepping, we lead into the half-time steps to separate the original coupling problem into three subproblems, implement two-level decoupling to simplify the complexity of solving coupling systems. Before that, the matrix and microfracture equations on the half-time steps in the dual-porosity media are calculated first, with the aim of replacing the initial values of the decoupling equations. Besides, for the nonlinear convection term in Navier–Stokes equations, the modified characteristic finite element method is chosen to avoid the problem of low computational efficiency. The convergence of the decoupling algorithm is rigorously derived by using the idea of mathematical induction. Finally, the reliability of the theoretical analysis and the rationality of the scheme are verified by numerical experiments.