A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows
A variational multiscale stabilized finite element method for the solution of the Euler equations of nonhydrostatic stratified flows
复制标题
求解非静水分层流欧拉方程的变分多尺度稳定有限元法
DOI：
10.1016/j.jcp.2012.10.056
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
G. Houzeaux
中科院分区：
文献类型：
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作者：
S. Marras;M. Moragues;M. Vázquez;O. Jorba;G. Houzeaux
我们提出了一个可压缩版本的变分多尺度稳定化（VMS）方法应用于非静力分层流的欧拉方程的有限元（FE）解。本文的目的是验证如何执行的算法时，解决非静力大气动力学的框架中的问题。这一努力是合理的VMS的先前观察到的良好性能，并通过一个紧凑的Galerkin公式提供的大规模并行架构的优势-计算流体动力学（CFD）和数值天气预报（NWP）从业者的范例。我们还提出了一个简单的技术来构建一个平衡的近似占主导地位的流体静力学，如果不适当的离散化，可能会导致不可接受的垂直振荡。这是数值预报中的一个相关问题，特别是在接近陡峭地形的地方。为了评估分层环境中的方法的性能，选择了六个标准的2D和两个3D测试用例。其中，两个承认一个半解析解，而其余六个是非稳态和非线性的热问题与占主导地位的浮力效应，挑战算法的稳定性。
We present a compressible version of the variational multiscale stabilization (VMS) method applied to the finite element (FE) solution of the Euler equations for nonhydrostatic stratified flows. This paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics. This effort is justified by the previously observed good performance of VMS and by the advantages that a compact Galerkin formulation offers on massively parallel architectures – a paradigm for both computational fluid dynamics (CFD) and numerical weather prediction (NWP) practitioners. We also propose a simple technique to construct a well-balanced approximation of the dominant hydrostatics that, if not properly discretized, may cause unacceptable vertical oscillations. This is a relevant problem in NWP, especially in the proximity of steep topography. To evaluate the performance of the method for stratified environments, six standard 2D and two 3D test cases are selected. Of these, two admit a semi-analytic solution, while the remaining six are non-steady and non-linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability.