A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier-Stokes equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:422

Article

Chen, Xi¹  Li, Yuwen²  Drapaca, Corina³  Cimbala, John¹ 

[1] Penn State Univ, Dept Mech Engn, University Pk, PA 16802 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Penn State Univ, Dept Engn Sci & Mech, University Pk, PA 16802 USA

关键词: Incompressible Navier-Stokes equation;    Discontinuous Galerkin method;    Mixed finite element method;    Energy stability;    Implicit Runge-Kutta methods;    Pressure robustness;   

DOI  :  10.1016/j.jcp.2020.109799

来源: Elsevier

【 摘 要 】

In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier-Stokes equation which yields the H-1-, H(div)-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge-Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor-Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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