Computational fluid dynamics and aerodynamics, which complement more expensive empirical approaches, are critical for developing aerospace vehicles. During the past three decades, computational aerodynamics capability has improved remarkably, following advances in computer hardware and algorithm development. However, for complex applications, the demands on computational fluid dynamics continue to increase in a quest to gain a few percent improvements in accuracy. Herein, we numerically demonstrate that optimizing the metric terms which arise from smoothly mapping each cell to a reference element, lead to a solution whose accuracy is practically never worse and often noticeably better than the one obtained using the widely adopted Thomas and Lombard metric terms computation (Geometric conservation law and its application to flow computations on moving grids, AIAA Journal, 1979). Low and high-order accurate entropy stable schemes on distorted, high-order tensor product elements are used to simulate three-dimensional inviscid and viscous compressible test cases for which an analytical solution is known.

中文翻译：

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满足自由流保存的优化几何度量

计算流体动力学和空气动力学是对更昂贵的经验方法的补充，对于开发航空航天器至关重要。在过去的三年中，随着计算机硬件和算法开发的进步，计算空气动力学能力得到了显着提高。然而，对于复杂的应用程序，对计算流体动力学的需求不断增加，以寻求在精度上获得几个百分点的改进。在这里，我们通过数值证明优化由平滑地将每个单元格映射到参考元素而产生的度量项，导致的解决方案的准确性实际上永远不会差，并且通常明显优于使用广泛采用的 Thomas 和 Lombard 度量项计算（几何守恒定律及其在移动网格上的流动计算中的应用，AIAA 期刊，1979 年）获得的解决方案。扭曲的高阶张量积元素的低阶和高阶精确熵稳定方案用于模拟三维无粘性和粘性可压缩测试用例，其解析解是已知的。