A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:356

Article

Piatkowski, Marian¹  Muthing, Steffen¹  Bastian, Peter¹ 

[1] Heidelberg Univ, Interdisciplinary Ctr Sci Comp, D-69120 Heidelberg, Germany

关键词: Navier-Stokes equations;    High-order discontinuous Galerkin;    Projection methods;    Incompressibility;   

DOI  :  10.1016/j.jcp.2017.11.035

来源: Elsevier

【 摘 要 】

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H(div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability. (c) 2017 Elsevier Inc. All rights reserved.

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