5.3.2 Upwind Schemes 上风格式[cfd-5-3-2]

至少就目前而言，上风格式在非结构网格上似乎比上述中心格式更受欢迎。实际上,Roe的通量差分分裂格式[50]是非结构网格上应用最广的方法。与中心格式相比，它对边界层的分辨率明显更高，对网格扭曲的敏感性更低，这正是Roe格式吸引人的地方。然而，性能改善的代价是更大的计算量——当必须使用限制器来抑制解的振荡时(5.3.5小节)，这一代价变得相当可观。en

Upwind schemes seem to have gained, at least for the moment, much more popularity on unstructured grids than the above central scheme. In fact, the flux-difference splitting scheme of Roe [50] is the most widely employed approach on unstructured grids. It is the considerably more accurate resolution of boundary layers and the lower sensitivity to grid distortions in comparison to the central scheme, which explains the attractiveness of Roe's scheme. However, the price to be paid for the improved performance is the higher computational effort, which becomes quite significant if a limiter has to be used to suppress oscillations of the solution (Subsection 5.3.5).

4.3节中针对结构网格介绍的各种上风格式，无需改动基本方法学即可用于非结构网格。只有左、右状态的计算(式(5.22))——即所谓的解重构——以及限制函数的计算需要新的公式。因此，这里只讨论解重构与限制器。关于各种上风方法的细节，读者可参阅4.3.2-4.3.4小节。采用中点对偶方法在非结构网格上实现Roe格式的例子可参见例如文献[33]。en

Any of the upwind schemes presented in Section 4.3 for structured grids are applicable to unstructured grids without modifications to the basic methodology. Only the computation of the left and right state (Eq. (5.22)), which is denoted as solution reconstruction, as well as the evaluation of the limiting function require new formulations. For this reason, only the solution reconstruction and the limiters are discussed here. For details on the various upwind methods, the reader is referred to Subsections 4.3.2-4.3.4. An example for the implementation of Roe's scheme on unstructured grids using the median-dual approach can be found, e.g., in Ref. [33].