Abstract A hoped-for outcome from high-order CFD methods, in addition to achieving accurate solutions on fine grids, is to achieve useful answers on coarse grids. In this paper we note that this outcome is by no means automatic, and consider how the different quests of accuracy and bandwidth may be achieved. Although accuracy is exclusively a low-frequency property and so amenable to Taylor series analysis, bandwidth is concerned with higher frequencies and may not be approachable by this route. It is argued that an important aspect should be the physically correct flow of information, especially for hyperbolic problems, and that this is strongly influenced by the choice of computational stencil. This is confirmed by applying von Neumann analysis to the linear advection equation, giving a strong preference to odd-order fully discrete schemes using upwind-biased stencils. However, it is pointed out that these schemes do not always generalize to higher dimensions, and a method is shown that achieves very accurate directionality even on unstructured grids. This is accomplished by taking information from the exact solution to the multidimensional IVP for acoustics.

中文翻译：

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为带宽设计 CFD 方法 - 一种物理方法

摘要 除了在细网格上获得精确解之外，高阶 CFD 方法所期望的结果是在粗网格上获得有用的答案。在本文中，我们注意到这个结果绝不是自动的，并考虑如何实现精度和带宽的不同要求。虽然精度完全是低频特性，因此适合泰勒级数分析，但带宽与更高频率有关，并且可能无法通过这条路线接近。有人认为，一个重要的方面应该是物理上正确的信息流，尤其是对于双曲线问题，并且这受到计算模板选择的强烈影响。这通过对线性平流方程应用冯诺依曼分析得到证实，强烈偏爱使用逆风偏置模板的奇数阶完全离散方案。然而，指出这些方案并不总是推广到更高的维度，并且显示了一种即使在非结构化网格上也能实现非常准确的方向性的方法。这是通过从声学多维 IVP 的精确解中获取信息来实现的。