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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:301

Article

Marras, Simone¹  Nazarov, Murtazo²  Giraldo, Francis X.¹ 

[1] Naval Postgrad Sch, Dept Appl Math, Monterey, CA USA

[2] Uppsala Univ, Dept Informat Technol, Uppsala, Sweden

关键词: Large eddy simulation;    LES;    Dynamic SGS model;    Adaptive dissipation;    Localized artificial viscosity;    Spectral element method;    Discontinuous Galerkin;    Low Mach number;    Stratified flows;    Non-hydrostatic atmospheric flows;   

DOI  :  10.1016/j.jcp.2015.07.034

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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