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

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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 focu...

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Hauptverfasser: Piatkowski, Stephan-Marian (VerfasserIn) , Müthing, Steffen (VerfasserIn) , Bastian, Peter (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2018
In: Journal of computational physics
Year: 2017, Jahrgang: 356, Pages: 220-239
ISSN:1090-2716
DOI:10.1016/j.jcp.2017.11.035
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jcp.2017.11.035
Verlag, lizenzpflichtig, Volltext: http://www.sciencedirect.com/science/article/pii/S0021999117308732
Volltext
Verfasserangaben:Marian Piatkowski, Steffen Müthing, Peter Bastian
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Zusammenfassung: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.
Beschreibung:Available online: 5 December 2017
Gesehen am 21.04.2020
Beschreibung:Online Resource
ISSN:1090-2716
DOI:10.1016/j.jcp.2017.11.035

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