Well balanced finite volume methods for nearly hydrostatic flows
Well balanced finite volume methods for nearly hydrostatic flows
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DOI：
10.1016/j.jcp.2003.11.008
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发表时间：
2004-05
影响因子：
4.1
通讯作者：
Nicola Botta;R. Klein;Susanne Langenberg;Susanne Lützenkirchen;F.-W Gerstengarbe;U. Werner
中科院分区：
文献类型：
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作者：
Nicola Botta;R. Klein;Susanne Langenberg;Susanne Lützenkirchen;F.-W Gerstengarbe;U. Werner
在近静力流动的数值近似中，主要静力平衡的适当表示是至关重要的：不平衡的截断误差会导致不可接受的伪运动，例如，在数值天气预报(NWP)模式的动力核心，特别是在陡峭的地形附近。在这篇文章中，我们开发了一种新的策略，用于构造相对于主导流体静力学而言是“良好平衡”的离散化。根据压力与平衡背景分布的偏差建立动量平衡的经典思想在这里是通过局部的、依赖于时间的流体静力重建来实现的。压力梯度和引力源项的平衡离散是通过“离散的阿基米德浮力原理”实现的。这一策略被应用于对可压缩流动的显式标准有限体积Godunov型格式进行最小修改的扩展。所得到的方法具有以下特征：(I)它继承了基础基本方案的守恒性质。(Ii)即使在曲线网格上，对于一大类近静力流动，它也是精确平衡的。(Iii)在不考虑为整个垂直空气柱定义的背景状态的情况下，求解完全可压缩流动方程。(4)对于实施细节，例如斜率限制函数的选择，或边界条件离散化的特殊性，它是稳健的。
In numerical approximations of nearly hydrostatic flows, a proper representation of the dominant hydrostatic balance is of crucial importance: unbalanced truncation errors can induce unacceptable spurious motions, e.g., in dynamical cores of models for numerical weather prediction (NWP) in particular near steep topography. In this paper we develop a new strategy for the construction of discretizations that are “well-balanced” with respect to dominant hydrostatics. The classical idea of formulating the momentum balance in terms of deviations of pressure from a balanced background distribution is realized here through local, time dependent hydrostatic reconstructions. Balanced discretizations of the pressure gradient and of the gravitation source term are achieved through a “discrete Archimedes' buoyancy principle”. This strategy is applied to extend an explicit standard finite volume Godunov-type scheme for compressible flows with minimal modifications. The resulting method has the following features: (i) It inherits its conservation properties from the underlying base scheme. (ii) It is exactly balanced, even on curvilinear grids, for a large class of near-hydrostatic flows. (iii) It solves the full compressible flow equations without reference to a background state that is defined for an entire vertical column of air. (iv) It is robust with respect to details of the implementation, such as the choice of slope limiting functions, or the particularities of boundary condition discretizations.