Staggered DG method for coupling of the stokes and darcy-forchheimer problems

Lina Zhao; Eric T. Chung; Eun Jae Park; Guanyu Zhou

doi:10.1137/19M1268525

Staggered DG method for coupling of the stokes and darcy-forchheimer problems

Lina Zhao, Eric T. Chung, Eun Jae Park, Guanyu Zhou

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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, and in addition, it is a good candidate for practical applications.

Original language	English
Pages (from-to)	1-31
Number of pages	31
Journal	SIAM Journal on Numerical Analysis
Volume	59
Issue number	1
DOIs	https://doi.org/10.1137/19M1268525
Publication status	Published - 2021

Bibliographical note

Funding Information:
\ast Received by the editors June 14, 2019; accepted for publication (in revised form) August 31, 2020; published electronically January 4, 2021. https://doi.org/10.1137/19M1268525 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was partially supported by the Hong Kong RGC General Research Fund projects 14304217, 14302018, the CUHK Faculty of Science Direct grant 2018-19, and the NSFC/RGC Joint Research Scheme project HKUST620/15. The work of the third author was supported by the NRF grants 2015R1A5A1009350, 2019R1A2C2090021. The work of the fourth author was supported by the JSPS grant KAKENHI 18K13460 and JSPS A3 Foresight Program \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, Hong Kong (lzhao@math.cuhk.edu.hk, tschung@math.cuhk.edu.hk).

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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title = "Staggered DG method for coupling of the stokes and darcy-forchheimer problems",

abstract = "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 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, and in addition, it is a good candidate for practical applications. ",

author = "Lina Zhao and Chung, {Eric T.} and Park, {Eun Jae} and Guanyu Zhou",

note = "Funding Information: \ast Received by the editors June 14, 2019; accepted for publication (in revised form) August 31, 2020; published electronically January 4, 2021. https://doi.org/10.1137/19M1268525 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was partially supported by the Hong Kong RGC General Research Fund projects 14304217, 14302018, the CUHK Faculty of Science Direct grant 2018-19, and the NSFC/RGC Joint Research Scheme project HKUST620/15. The work of the third author was supported by the NRF grants 2015R1A5A1009350, 2019R1A2C2090021. The work of the fourth author was supported by the JSPS grant KAKENHI 18K13460 and JSPS A3 Foresight Program \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, Hong Kong (lzhao@math.cuhk.edu.hk, tschung@math.cuhk.edu.hk). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics.",

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doi = "10.1137/19M1268525",

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AU - Zhou, Guanyu

N1 - Funding Information: \ast Received by the editors June 14, 2019; accepted for publication (in revised form) August 31, 2020; published electronically January 4, 2021. https://doi.org/10.1137/19M1268525 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was partially supported by the Hong Kong RGC General Research Fund projects 14304217, 14302018, the CUHK Faculty of Science Direct grant 2018-19, and the NSFC/RGC Joint Research Scheme project HKUST620/15. The work of the third author was supported by the NRF grants 2015R1A5A1009350, 2019R1A2C2090021. The work of the fourth author was supported by the JSPS grant KAKENHI 18K13460 and JSPS A3 Foresight Program \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, Hong Kong (lzhao@math.cuhk.edu.hk, tschung@math.cuhk.edu.hk). Publisher Copyright: © 2021 Society for Industrial and Applied Mathematics.

PY - 2021

Y1 - 2021

N2 - 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, and in addition, it is a good candidate for practical applications.

AB - 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, and in addition, it is a good candidate for practical applications.

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Staggered DG method for coupling of the stokes and darcy-forchheimer problems

Abstract

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