We present an overview of recent developments on the convergence analysis of numerical methods for inviscid multidimensional compressible flows that preserve underlying physical structures. We introduce the concept of generalized solutions, the so-called dissipative solutions, and explain their relationship to other commonly used solution concepts. In numerical experiments we apply K-convergence of numerical solutions and approximate turbulent solutions together with the Reynolds stress defect and the energy defect.

翻译：我们综述了近年来关于保持内在物理结构的无粘多维可压缩流数值方法收敛性分析的最新进展。引入了广义解的概念，即所谓的耗散解，并阐释了其与其他常用解概念之间的关系。在数值实验中，我们应用了数值解的K-收敛性和近似湍流解，并结合了雷诺应力缺陷与能量缺陷。