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

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Title: A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows
Authors: Marras, Simone1 simone.marras@bsc.es, Moragues, Margarida1, Vázquez, Mariano1,2 mariano.vazquez@bsc.es, Jorba, Oriol1, Houzeaux, Guillaume1
Source: Journal of Computational Physics. Mar2013, Vol. 236, p380-407. 28p.
Subjects: Finite element method, Euler equations, Hydrostatics, Algorithms, Computational fluid dynamics, Buoyancy
Abstract: 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. [Copyright &y& Elsevier]
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Database: Engineering Source
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Abstract: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. [Copyright &y& Elsevier]
ISSN:00219991
DOI:10.1016/j.jcp.2012.10.056