A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains

Sander Rhebergen, Bernardo Cockburn

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73 Scopus citations

Abstract

We present the first space-time hybridizable discontinuous Galerkin (HDG) finite element method for the incompressible Navier-Stokes and Oseen equations. Major advantages of a space-time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher-order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space-time elements. Our formulation is related to the HDG formulation for incompressible flows introduced recently in, e.g., [N.C. Nguyen, J. Peraire, B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow, Comput. Methods Appl. Mech. Eng. 199 (2010) 582-597]. However, ours is inspired in typical DG formulations for compressible flows which allow for a more straightforward implementation. Another difference is the use of polynomials of fixed total degree with space-time hexahedral and quadrilateral elements, instead of simplicial elements. We present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time.

Original languageEnglish (US)
Pages (from-to)4185-4204
Number of pages20
JournalJournal of Computational Physics
Volume231
Issue number11
DOIs
StatePublished - Jun 1 2012

Keywords

  • Deforming domains
  • Incompressible Navier-Stokes
  • Oseen equations
  • Space-time hybridizable discontinuous Galerkin method

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