A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows

Simone Marras, Margarida Moragues, Mariano Vázquez, Oriol Jorba, Guillaume Houzeaux

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14 Scopus citations

Abstract

We present a compressible version of the variational multiscale stabilization (VMS) method applied to the finite element (FE) solution of the Euler equations for nonhydrostatic stratified flows. This paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics. This effort is justified by the previously observed good performance of VMS and by the advantages that a compact Galerkin formulation offers on massively parallel architectures - a paradigm for both computational fluid dynamics (CFD) and numerical weather prediction (NWP) practitioners. We also propose a simple technique to construct a well-balanced approximation of the dominant hydrostatics that, if not properly discretized, may cause unacceptable vertical oscillations. This is a relevant problem in NWP, especially in the proximity of steep topography. To evaluate the performance of the method for stratified environments, six standard 2D and two 3D test cases are selected. Of these, two admit a semi-analytic solution, while the remaining six are non-steady and non-linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability.

Original languageEnglish (US)
Pages (from-to)380-407
Number of pages28
JournalJournal of Computational Physics
Volume236
Issue number1
DOIs
StatePublished - Mar 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Euler equations
  • Finite element method
  • Nonhydrostatic flows
  • Variational multiscale stabilization

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