A stabilization for three‐dimensional discontinuous Galerkin discretizations applied to nonhydrostatic atmospheric simulations
A stabilization for three‐dimensional discontinuous Galerkin discretizations applied to nonhydrostatic atmospheric simulations
复制标题
应用于非静水大气模拟的三维不连续伽辽金离散化的稳定性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
É. Deleersnijder
中科院分区：
文献类型：
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作者：
S. Blaise;J. Lambrechts;É. Deleersnijder
一个不连续的Galerkin非静力大气模式用于二维和三维模拟。需要处理的时间跨度很大。为此，实现了两种不同的隐式/显式时间离散化。基于重力项的降阶离散化，引入了稳定化，以确保压力和重力效应之间的平衡。虽然不影响显着的收敛性能的计划，这种方法允许模拟各向异性流，而不会产生虚假的振荡，因为它发生在一个经典的不连续Galerkin离散。这种方法被证明是扩散比通常的空间滤波器。一个稳定性分析表明，使用这种修改后的计划放弃与通常的离散化的不稳定性。对解析解进行验证，证实了良好的收敛性和稳定性的计划。数值结果证明了隐/显时间积分间断Galerkin方法对大尺度大气流动的吸引性。版权所有© 2015约翰威利父子有限公司.
A discontinuous Galerkin nonhydrostatic atmospheric model is used for two‐dimensional and three‐dimensional simulations. There is a wide range of timescales to be dealt with. To do so, two different implicit/explicit time discretizations are implemented. A stabilization, based upon a reduced‐order discretization of the gravity term, is introduced to ensure the balance between pressure and gravity effects. While not affecting significantly the convergence properties of the scheme, this approach allows the simulation of anisotropic flows without generating spurious oscillations, as it happens for a classical discontinuous Galerkin discretization. This approach is shown to be less diffusive than usual spatial filters. A stability analysis demonstrates that the use of this modified scheme discards the instability associated with the usual discretization. Validation against analytical solutions is performed, confirming the good convergence and stability properties of the scheme. Numerical results demonstrate the attractivity of the discontinuous Galerkin method with implicit/explicit time integration for large‐scale atmospheric flows. Copyright © 2015 John Wiley & Sons, Ltd.
用于波动方程的水平显式/垂直隐式 (HEVI) 解的 Runge-Kutta IMEX 方案
影响因子：
4.1
作者：
Weller H
通讯作者：
Weller H