Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES
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Authors
Marras, Simone
Nazarov, Murtazo
Giraldo, Francis X.
Subjects
Advisors
Date of Issue
2015
Date
Publisher
Association for Computing Machinery (ACM)
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Abstract
The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1016/j.jcp.2015.07.034
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
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NPS Report Number
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Format
40 p.
Citation
S. Marras, M. Nazarov, F.X. Giraldo, "Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES," Journal of Computational Physics, v. 301, (January 2015), pp. 77-101
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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.