Fully-conservative High-order FR Scheme on Moving and Deforming Grids
Fully-conservative High-order FR Scheme on Moving and Deforming Grids
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DOI：
10.2514/6.2015-2745
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Yoshiaki Abe;T. Haga;T. Nonomura;K. Fujii
中科院分区：
文献类型：
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作者：
Yoshiaki Abe;T. Haga;T. Nonomura;K. Fujii
在高阶守恒通量重构格式中，给出了构造对称守恒度量的适当步骤。本框架使一个直接离散化的强保守形式的控制方程，没有任何错误的自由度保存和全局守恒性质的三维移动和变形网格。我们表明，一个简单的实现对称保守度量往往无法构建度量多项式的解多项式，这严重降低了数值精度相同的顺序。另一方面，通过适当的程序构造的对称保守度量可以保持自由的解决方案，而不管形状函数的顺序;此外，对流涡更准确地计算变形网格。在变形网格上数值模拟对流涡的全局守恒性。
An appropriate procedure to construct the symmetric conservative metrics is presented in the high-order conservative flux-reconstruction scheme. The present framework enables a direct discretization of the strong conservation form of governing equations without any errors in the freestream preservation and global conservation properties on threedimensionally moving and deforming grids. We show that a straightforward implementation of the symmetric conservative metrics often fails to construct metric polynomials with the same order of a solution polynomial, which severely degrades a numerical accuracy. On the other hand, the symmetric conservative metrics constructed by the appropriate procedure can preserve the freestream solution regardless of the order of shape functions; in addition, a convecting vortex is more accurately computed on deforming grids. The global conservation property is also demonstrated numerically for the convecting vortex on deforming grids.