An hp-adaptive discontinuous Galerkin method for shallow water flows

C. Eskilsson*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

25 Citations (Scopus)

Abstract

An adaptive spectral/hp discontinuous Galerkin method for the two-dimensional shallow water equations is presented. The model uses an orthogonal modal basis of arbitrary polynomial order p defined on unstructured, possibly non-conforming, triangular elements for the spatial discretization. Based on a simple error indicator constructed by the solutions of approximation order p and p-1, we allow both for the mesh size, h, and polynomial approximation order to dynamically change during the simulation. For the h-type refinement, the parent element is subdivided into four similar sibling elements. The time-stepping is performed using a third-order Runge-Kutta scheme. The performance of the hp-adaptivity is illustrated for several test cases. It is found that for the case of smooth flows, p-adaptivity is more efficient than h-adaptivity with respect to degrees of freedom and computational time.

Original languageEnglish
JournalInternational Journal for Numerical Methods in Fluids
Volume67
Issue number11
Pages (from-to)1605-1623
Number of pages19
ISSN0271-2091
DOIs
Publication statusPublished - 20 Dec 2011
Externally publishedYes

Keywords

  • Adaptivity
  • Discontinuous Galerkin method
  • High-order
  • Non-conforming elements
  • Shallow water equations

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