Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

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Author
Marras, Simone
Nazarov, Murtazo
Giraldo, Francis X.
Date
2015Metadata
Show full item recordAbstract
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.
Description
The article of record as published may be found at http://dx.doi.org/10.1016/j.jcp.2015.07.034