Staggered DG method for coupling of the Stokes and Darcy-Forchheimer problems

TL;DR

This paper introduces a staggered discontinuous Galerkin method for coupled Stokes and Darcy-Forchheimer problems, effectively handling complex grids and interface conditions with proven optimal convergence and demonstrated numerical accuracy.

Contribution

The paper presents a novel staggered DG method that simplifies interface treatment and is adaptable to irregular grids for coupled flow problems.

Findings

Method achieves optimal convergence rates.

Effective on distorted and polygonal grids.

Numerical experiments confirm accuracy and efficiency.

Abstract

In this paper we develop a staggered discontinuous Galerkin method for the Stokes and Darcy-Forchheimer problems coupled with the \Red{Beavers-Joseph-Saffman} conditions. The method is defined by imposing staggered continuity for all the variables involved and the interface conditions are enforced by switching the roles of the variables met on the interface, which eliminate the hassle of introducing additional variables. This method can be flexibly applied to rough grids such as the highly distorted grids and the polygonal grids. In addition, the method allows nonmatching grids on the interface thanks to the special inclusion of the interface conditions, which is highly appreciated from a practical point of view. A new discrete trace inequality and a generalized Poincar\'{e}-Friedrichs inequality are proved, which enables us to prove the optimal convergence estimates under reasonable regularity assumptions. Finally, several numerical experiments are given to illustrate the performances of the proposed method, and the numerical results indicate that the proposed method is accurate and efficient, in addition, it is a good candidate for practical applications.