A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density

Buyang Li; Weifeng Qiu; Zongze Yang

doi:10.1007/s10915-022-01775-1

A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density

Buyang Li, Weifeng Qiu, Zongze Yang

Department of Applied Mathematics

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier–Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is solved by an H ¹-conforming finite element method, and an upwind discontinuous Galerkin finite element method with post-processed velocity is adopted for the density equation. The proposed method is proved to be convergent in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.

Original language	English
Article number	2
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Scientific Computing
Volume	91
Issue number	1
DOIs	https://doi.org/10.1007/s10915-022-01775-1
Publication status	Published - Apr 2022

Keywords

Discontinuous Galerkin methods
Navier–Stokes equations
Transport equation
Variable density

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

More information

10.1007/s10915-022-01775-1

Cite this

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abstract = "We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier–Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is solved by an H 1-conforming finite element method, and an upwind discontinuous Galerkin finite element method with post-processed velocity is adopted for the density equation. The proposed method is proved to be convergent in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.",

keywords = "Discontinuous Galerkin methods, Navier–Stokes equations, Transport equation, Variable density",

author = "Buyang Li and Weifeng Qiu and Zongze Yang",

note = "Funding Information: The work of B. Li and Z. Yang was supported in part by National Natural Science Foundation of China (NSFC Grant 12071020) and an internal grant of The Hong Kong Polytechnic University (Project 4-ZZKQ). Weifeng Qiu is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11302718). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Qiu, Weifeng

AU - Yang, Zongze

N1 - Funding Information: The work of B. Li and Z. Yang was supported in part by National Natural Science Foundation of China (NSFC Grant 12071020) and an internal grant of The Hong Kong Polytechnic University (Project 4-ZZKQ). Weifeng Qiu is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11302718). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

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N2 - We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier–Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is solved by an H 1-conforming finite element method, and an upwind discontinuous Galerkin finite element method with post-processed velocity is adopted for the density equation. The proposed method is proved to be convergent in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.

AB - We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier–Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is solved by an H 1-conforming finite element method, and an upwind discontinuous Galerkin finite element method with post-processed velocity is adopted for the density equation. The proposed method is proved to be convergent in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.

KW - Discontinuous Galerkin methods

KW - Navier–Stokes equations

KW - Transport equation

KW - Variable density

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DO - 10.1007/s10915-022-01775-1

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A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density

Abstract

Keywords

ASJC Scopus subject areas

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