Abstract

This paper considers the construction of a generalized computational experiment for solving verification problems. The problem of comparative accuracy assessment of numerical methods is currently acquiring special relevance due to the introduction of published standards and widespread use of software packages that include a large number of different solvers. A generalized computational experiment makes it possible to obtain a numerical solution for a class of problems determined by variation ranges of their governing parameters. Analysis of results represented as multidimensional arrays, where the number of measurements depends on the dimension of the space of governing parameters, requires the use of scientific visualization and visual analytics tools. Some approaches to the application of generalized computational experiments with and without a reference solution are discussed. An example of constructing error surfaces when comparing some solvers from the OpenFOAM software package is considered. The classical problem of an inviscid oblique shock wave is used as a basic problem. Certain variations of its main parameters—Mach number and angle of attack—are analyzed. In addition, we consider an example of the cone flow problem with variable Mach number, cone angle, and angle of attack. The concept of an error index is introduced as an integral characteristic of deviations from the exact solution for each solver in the class of problems under consideration.

中文翻译：

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广义计算实验与验证问题

摘要

本文考虑构建一个用于解决验证问题的广义计算实验。由于已发布标准的引入和包含大量不同求解器的软件包的广泛使用，数值方法的比较精度评估问题目前具有特殊的相关性。广义计算实验使得获得由其控制参数的变化范围确定的一类问题的数值解成为可能。对表示为多维数组的结果进行分析，其中测量次数取决于控制参数空间的维度，需要使用科学可视化和可视化分析工具。讨论了在有和没有参考解决方案的情况下应用广义计算实验的一些方法。考虑比较 OpenFOAM 软件包中的一些求解器时构造误差曲面的示例。无粘性斜激波的经典问题被用作基本问题。分析了其主要参数（马赫数和攻角）的某些变化。此外，我们还考虑了具有可变马赫数、锥角和攻角的锥流问题的示例。误差指数的概念被引入作为所考虑的问题类别中每个求解器的精确解偏差的积分特征。考虑比较 OpenFOAM 软件包中的一些求解器时构造误差曲面的示例。无粘性斜激波的经典问题被用作基本问题。分析了其主要参数（马赫数和攻角）的某些变化。此外，我们还考虑了具有可变马赫数、锥角和攻角的锥流问题的示例。误差指数的概念被引入作为所考虑的问题类别中每个求解器的精确解的偏差的积分特征。考虑比较 OpenFOAM 软件包中的一些求解器时构造误差曲面的示例。无粘性斜激波的经典问题被用作基本问题。分析了其主要参数（马赫数和攻角）的某些变化。此外，我们还考虑了具有可变马赫数、锥角和攻角的锥流问题的示例。误差指数的概念被引入作为所考虑的问题类别中每个求解器的精确解偏差的积分特征。锥角和攻角。误差指数的概念被引入作为所考虑的问题类别中每个求解器的精确解偏差的积分特征。锥角和攻角。误差指数的概念被引入作为所考虑的问题类别中每个求解器的精确解偏差的积分特征。