Two-grid domain decomposition methods for the coupled Dual-Porosity-Navier-Stokes system with Beavers-Joseph interface condition

Abstract

In this paper, two kinds of two-grid domain decomposition methods for the coupled Dual-Porosity-Navier-Stokes system are proposed and analyzed by integrating the established robin-type domain decomposition approach with a two-grid strategy. Initially, we apply the established robin-type domain decomposition approach on a coarse grid to address the coupled problem. Subsequently, on a fine grid, we employ two distinct approaches: first, to solve the matrix and microfracture subproblems, followed by the Navier–Stokes subproblem. Both approaches fundamentally approximate the interface term using the coarse-grid solution. The proposed algorithms integrate the two-grid approach with the established domain decomposition method, capitalizing on the strengths of both techniques while addressing their respective limitations. Comprehensive theoretical analysis is established, and four in-depth numerical investigations are conducted to assess the efficiency, accuracy, and robustness of the proposed algorithms by comparing them with the domain decomposition method.