Towards a geometric variational discretization of compressible fluids: the rotating shallow water equations
Towards a geometric variational discretization of compressible fluids: the rotating shallow water equations
复制标题
可压缩流体的几何变分离散化：旋转浅水方程
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
F. Gay
中科院分区：
文献类型：
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作者：
W. Bauer;F. Gay
本文提出了可压缩流体动力学的几何变分离散化。数值格式是通过以结构保持方式离散微分同胚群上的流体动力学李群公式和相关变分原理而获得的。我们的框架适用于 2D 和 3D 中的不规则网格离散化。它将以前针对不可压缩流体所做的工作系统地扩展到可压缩情况。我们详细考虑了二维不规则单纯网格的数值格式，并针对旋转浅水方程对该格式进行了数值评估。特别是，我们研究了该方案是否守恒稳态解、能否很好地表示非线性动力学、是否能很好地近似连续方程的频率关系，同时保留质量和总能量等守恒定律。
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in detail the numerical scheme on 2D irregular simplicial meshes and evaluate the scheme numerically for the rotating shallow water equations. In particular, we investigate whether the scheme conserves stationary solutions, represents well the nonlinear dynamics, and approximates well the frequency relations of the continuous equations, while preserving conservation laws such as mass and total energy.
多边形球面网格旋转浅水方程的原-对偶拟态有限元格式
DOI：
10.48550/arxiv.1409.8130
发表时间：
2014
期刊：
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影响因子：
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作者：
Thuburn J
通讯作者：
Thuburn J