Robust and accurate viscous discretization via upwind scheme – I: Basic principle
Robust and accurate viscous discretization via upwind scheme – I: Basic principle
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DOI：
10.1016/j.compfluid.2011.04.014
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发表时间：
2011-10
影响因子：
2.8
通讯作者：
H. Nishikawa
中科院分区：
文献类型：
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作者：
H. Nishikawa
在本文中，我们介绍了一个一般原则，用于构建强大的和准确的粘性离散，这是适用于各种离散方法，包括有限体积，剩余分布，间断Galerkin，和谱体积方法。该原理基于粘性项的双曲模型。它是用对流格式离散双曲方程组，然后由结果导出粘性离散。所提出的原则的一个显着特点是，它会自动引入阻尼项到所产生的粘性计划，这是必不可少的有效的高频误差阻尼，在某些情况下，一致性也。在本文中，我们展示了一般原则的扩散方程的均匀网格在一维和非结构网格在二维，节点/单元中心有限体积，剩余分布，间断Galerkin，和谱体积方法。数值结果验证了导出的扩散格式的准确性，并说明了阻尼项的重要性，为高度倾斜的典型粘性网格。
In this paper, we introduce a general principle for constructing robust and accurate viscous discretization, which is applicable to various discretization methods, including finite-volume, residual-distribution, discontinuous-Galerkin, and spectral-volume methods. The principle is based on a hyperbolic model for the viscous term. It is to discretize the hyperbolic system by an advection scheme, and then derive a viscous discretization from the result. A distinguished feature of the proposed principle is that it automatically introduces a damping term into the resulting viscous scheme, which is essential for effective high-frequency error damping and, in some cases, for consistency also. In this paper, we demonstrate the general principle for the diffusion equation on uniform grids in one dimension and unstructured grids in two dimensions, for node/cell-centered finite-volume, residual-distribution, discontinuous-Galerkin, and spectral-volume methods. Numerical results are presented to verify the accuracy of the derived diffusion schemes and to illustrate the importance of the damping term for highly-skewed typical viscous grids.