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

• Verfasst von: Piatkowski, Stephan-Marian [VerfasserIn]
• Verfasst von: Müthing, Steffen [VerfasserIn]
• Verfasst von: Bastian, Peter [VerfasserIn]
• Titel: A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations
• Verf.angabe: Marian Piatkowski, Steffen Müthing, Peter Bastian
• Jahr: 2018
• Jahr des Originals: 2017
• Umfang: 20 S.
• Fussnoten: Available online: 5 December 2017 ; Gesehen am 21.04.2020
• Titel Quelle: Enthalten in: Journal of computational physics
• Ort Quelle: Amsterdam : Elsevier, 1961
• Jahr Quelle: 2018
• Band/Heft Quelle: 356(2018), Seite 220-239
• ISSN Quelle: 1090-2716
• DOI: doi:10.1016/j.jcp.2017.11.035
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High-order discontinuous Galerkin
• Sach-SW: Incompressibility
• Sach-SW: Navier-Stokes equations
• Sach-SW: Projection methods
• K10plus-PPN: 1695561597

Abstract

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.