Abstract

A family of high-order multioperator compact schemes for computation of viscous gas flows on curvilinear grids is considered. Depending on the number of operators used, the order of a scheme approximating the convective terms of the original equations can vary from the 6th to 22nd. The viscous terms and the metric coefficients of a generalized curvilinear coordinate system are approximated with the same order. An example of three schemes, including a five-operator one, which is the most computationally intensive in the described family, is used to examine their structure. The change in the approximation and dissipation properties of the schemes caused by an increase in their order is investigated. The schemes are used for comparative computations of subsonic gas flows based on the Euler and Navier–Stokes equations. Numerical results based on the 22nd-order scheme are presented for a viscous subsonic airfoil flow in a wide range of angles of attack and for an impermeable parachute canopy.

中文翻译：

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基于高阶复合紧凑格式的非稳态亚音速粘性气体流动的数值模拟

摘要

考虑了用于计算曲线网格上粘性气体流动的一系列高阶多算子紧凑型方案。根据使用的运算符的数量，近似原始方程式对流项的方案的阶数可以在6到22之间变化。广义曲线坐标系的粘性项和度量系数以相同的阶数近似。使用三个方案的示例，其中包括五个算子的方案，这是所描述系列中计算量最大的方案，用于检查其结构。研究了由于顺序增加而引起的近似和耗散特性的变化。该方案用于基于Euler和Navier–Stokes方程的亚音速气流的比较计算。