A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

doi:10.1007/s42967-020-00106-1

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (1): 205-226.doi: 10.1007/s42967-020-00106-1

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A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

Lina Zhao, Ming Fai Lam, Eric Chung

Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, China

收稿日期:2020-08-25 修回日期:2020-11-17 出版日期:2022-03-20 发布日期:2022-03-01
通讯作者: Eric Chung, Lina Zhao, Ming Fai Lam E-mail:tschung@math.cuhk.edu.hk;lzhao@math.cuhk.edu.hk;mfam@math.cuhk.edu.hk
基金资助:
The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304719 and 14302018) and CUHK Faculty of Science Direct Grant 2019-20.

A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

Lina Zhao, Ming Fai Lam, Eric Chung

Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, China

Received:2020-08-25 Revised:2020-11-17 Online:2022-03-20 Published:2022-03-01
Contact: Eric Chung, Lina Zhao, Ming Fai Lam E-mail:tschung@math.cuhk.edu.hk;lzhao@math.cuhk.edu.hk;mfam@math.cuhk.edu.hk
Supported by:
The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304719 and 14302018) and CUHK Faculty of Science Direct Grant 2019-20.

摘要/Abstract

摘要： In this paper, we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem. Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme can be fexibly applied to fairly general polygonal meshes. We relax the tangential continuity for velocity, which is the key ingredient in achieving the uniform robustness. We present well-posedness and error analysis for both the semi-discrete scheme and the fully discrete scheme, and the theories indicate that the error estimates for velocity are independent of pressure. Several numerical experiments are presented to confrm the theoretical fndings.

关键词: Staggered DG method, Brinkman-Forchheimer, General meshes, Uniformly stable

Abstract: In this paper, we propose and analyze a uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem. Our formulation is based on velocity gradient-velocity-pressure and the resulting scheme can be fexibly applied to fairly general polygonal meshes. We relax the tangential continuity for velocity, which is the key ingredient in achieving the uniform robustness. We present well-posedness and error analysis for both the semi-discrete scheme and the fully discrete scheme, and the theories indicate that the error estimates for velocity are independent of pressure. Several numerical experiments are presented to confrm the theoretical fndings.

Key words: Staggered DG method, Brinkman-Forchheimer, General meshes, Uniformly stable

中图分类号:

Lina Zhao, Ming Fai Lam, Eric Chung. A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem[J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 205-226.

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A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem

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