Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES
Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES
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基于 LES 无参数动态 SGS 模型的稳定高阶 Galerkin 方法
DOI：
10.1016/j.jcp.2015.07.034
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
F. Giraldo
中科院分区：
文献类型：
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作者：
S. Marras;Murtazo Nazarov;F. Giraldo
通过动态亚网格尺度模型（Dyn-SGS）稳定了欧拉方程的高阶谱元近似。该模型最初是为线性有限元设计的，用于求解大马赫数下的可压缩流。我们将其应用推广到高阶谱元，求解低马赫数分层流的欧拉方程。本文的主要工作有两个方面：稳定化和大涡模拟仅通过一个方案实现，由于Dyn-SGS得到的正则化应力的扩散系数是基于残差的，所以在解光滑的区域人工扩散的影响是最小的。直接的后果是，名义上的收敛速度的高阶光滑问题的解决方案是没有退化。据我们所知，这是第一次应用于大气模拟的谱元素模式稳定的涡粘性方案，通过建设，可以满足稳定的要求，可以模拟湍流通过LES，是完全自由的用户可调参数。它可以在不连续Galerkin、有限体积或其它类似环境中实现。初步间断Galerkin结果报告。还描述了非线性标量问题的直接扩展。一套1D，2D和3D的测试用例被用来评估的方法，与最知名的Lilly-Smagorinsky SGS模型所获得的结果进行了一些比较。
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.