An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:417

Article

Horvath, Tamas L.¹  Rhebergen, Sander² 

[1] Oakland Univ, Dept Math & Stat, Rochester, MI 48063 USA

[2] Univ Waterloo, Dept Appl Math, Waterloo, ON, Canada

关键词: Navier-Stokes;    Embedded;    Hybridized;    Discontinuous Galerkin;    Space-time;    Time-dependent domains;   

DOI  :  10.1016/j.jcp.2020.109577

来源: Elsevier

【 摘 要 】

This paper presents a space-time embedded-hybridized discontinuous Galerkin (EHDG) method for the Navier-Stokes equations on moving domains. This method uses a different hybridization compared to the space-time hybridized discontinuous Galerkin (HDG) method we presented previously in Horvath and Rhebergen (2019) [29]. In the space-time EHDG method the velocity trace unknown is continuous while the pressure trace unknown is discontinuous across facets. In the space-time HDG method, all trace unknowns are discontinuous across facets. Alternatively, we present also a space-time embedded discontinuous Galerkin (EDG) method in which all trace unknowns are continuous across facets. The advantage of continuous trace unknowns is that the formulation has fewer global degrees-of-freedom for a given mesh than when using discontinuous trace unknowns. Nevertheless, the discrete velocity field obtained by the space-time EHDG and EDG methods, like the space-time HDG method, is exactly divergence-free, even on moving domains. However, only the space-time EHDG and HDG methods result in divergence-conforming velocity fields. An immediate consequence of this is that the space-time EHDG and HDG discretizations of the conservative form of the Navier-Stokes equations are energy stable. The space-time EDG method, on the other hand, requires a skew-symmetric formulation of the momentum advection term to be energy-stable. Numerical examples will demonstrate the differences in solution obtained by the space-time EHDG, EDG, and HDG methods. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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