DeepAI AI Chat
Log In Sign Up

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

06/16/2019
by   Lina Zhao, et al.
Tokyo University of Science
Yonsei University
The Chinese University of Hong Kong
0

In this paper we develop a staggered discontinuous Galerkin method for the Stokes and Darcy-Forchheimer problems coupled with the 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 Poincaré-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.

READ FULL TEXT

page 22

page 24

page 26

page 27

page 28

08/29/2023

A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes/Biot problem

In this paper we present a hybridizable discontinuous Galerkin method fo...
11/20/2019

A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits

In this paper we propose a novel staggered discontinuous Galerkin method...
05/23/2019

An embedded--hybridized discontinuous Galerkin method for the coupled Stokes--Darcy system

We introduce an embedded--hybridized discontinuous Galerkin (EDG--HDG) m...
11/22/2022

The weak Galerkin finite element method for Stokes interface problems with curved interface

In this paper, we develop a new weak Galerkin finite element scheme for ...
12/07/2020

An eXtended HDG method for Darcy-Stokes-Brinkman interface problems

This paper proposes an interface/boundary-unfitted eXtended hybridizable...
09/30/2021

A Robin-type domain decomposition method for a novel mixed-type DG method for the coupled Stokes-Darcy problem

In this paper, we first propose and analyze a novel mixed-type DG method...
03/03/2022

A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions

A numerical method for coupled 3D-1D problems with discontinuous solutio...