A conservative discontinous Galerkin semi-implicit formulation for the Navier-Stokes equations in nonhydrostatic mesoscale modeling
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Authors
Restelli, Marco
Giraldo, Francis X.
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Date of Issue
2008
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Abstract
A Discontinuous Galerkin (DG) finite element formulation is proposed for the solution
of the compressible Navier–Stokes equations for a vertically stratified fluid, which are of interest
in mesoscale nonhydrostatic atmospheric modeling. The resulting scheme naturally ensures conservation
of mass, momentum and energy. A semi-implicit time integration approach is adopted to
improve the efficiency of the scheme with respect to explicit Runge–Kutta time integration strategies
usually employed in the context of DG formulations. A method is also presented to reformulate the
resulting linear system as a pseudo-Helmholtz problem. In doing this, we obtain a DG discretization
closely related to those proposed for the solution of elliptic problems, and we show how to take
advantage of numerical integration to increase the efficiency of the solution algorithm. The resulting
numerical formulation is then validated on a collection of classical two-dimensional test cases,
including density driven flows and mountain wave simulations.
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Article
Description
The article of record as published may be found at https://doi.org/10.1137/070708470
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School
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24 p.
Citation
M. Restelli, F.X. Giraldo
"A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling" SIAM Journal of Scientific Computing, v. 31,#3, (May 7, 2009), 2231–2257. (27 pages)
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.