SIAM Review, Volume 63, Issue 4, Page 756-779, January 2021.
It has been found advantageous for finite-volume discretizations of flow equations to possess additional (secondary) invariants, besides the (primary) invariants from the constituting conservation laws. This paper presents general (necessary and sufficient) requirements for a method to convectively preserve discrete kinetic energy. The key ingredient is a close discrete consistency between the convective term in the momentum equation and the terms in the other conservation equations (mass, internal energy). As examples, the Euler equations for subsonic (in)compressible flow are discretized with such supraconservative finite-volume methods on structured as well as unstructured grids.

中文翻译：

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亚音速可压缩流欧拉方程的超保守有限体积方法

SIAM Review，第 63 卷，第 4 期，第 756-779 页，2021
年1 月。已经发现，除了来自构成守恒定律的（主要）不变量之外，流动方程的有限体积离散化具有额外的（次要）不变量。本文介绍了对流保持离散动能的方法的一般（必要和充分）要求。关键因素是动量方程中的对流项与其他守恒方程（质量、内能）中的项之间的紧密离散一致性。例如，亚音速（非）可压缩流动的欧拉方程在结构化和非结构化网格上使用这种超保守有限体积方法进行离散化。