Capturing near-equilibrium solutions: A comparison between high-order discontinuous Galerkin methods and well-balanced schemes

Maria Han Veiga, David A. Velasco-Romero, Rémi Abgrall, Romain Teyssier

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Equilibrium or stationary solutions usually proceed through the exact balance between hyperbolic transport terms and source terms. Such equilibrium solutions are affected by truncation errors that prevent any classical numerical scheme from capturing the evolution of small amplitude waves of physical significance. In order to overcome this problem, we compare two commonly adopted strategies: going to very high order and reduce drastically the truncation errors on the equilibrium solution, or design a specific scheme that preserves by construction the equilibrium exactly, the so-called well-balanced approach. We present a modern numerical implementation of these two strategies and compare them in details, using hydrostatic but also dynamical equilibrium solutions of several simple test cases. Finally, we apply our methodology to the simulation of a protoplanetary disc in centrifugal equilibrium around its star and model its interaction with an embedded planet, illustrating in a realistic application the strength of both methods.

Original languageEnglish (US)
Pages (from-to)1-34
Number of pages34
JournalCommunications in Computational Physics
Volume26
Issue number1
DOIs
StatePublished - 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Keywords

  • Benchmark
  • Discontinuous Galerkin methods
  • Numerical methods
  • Well-balanced methods

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