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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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10.1016/j.jcp.2012.10.056
 
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Cita com:
hdl:2117/19333

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Marras, Simone
Moragues, Margarida
Vázquez, MarianoMés informació
Jorba Casellas, OriolMés informació
Houzeaux, GuillaumeMés informació
Document typeArticle
Defense date2013-03-01
Rights accessRestricted access - publisher's policy
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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.
CitationMarras, S. [et al.]. A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows. "Journal of computational physics", 01 Març 2013, vol. 236, p. 380-407. 
URIhttp://hdl.handle.net/2117/19333
DOI10.1016/j.jcp.2012.10.056
ISSN0021-9991
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S0021999112006626
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