SIAM Review, Volume 63, Issue 4, Page 721-721, January 2021.
The car-themed cover art on the current issue of SIAM Review is courtesy of the first of two Research Spotlights articles this issue. Indeed, the paper “Industry-Relevant Implicit Large-Eddy Simulation of a High-Performance Road Car via Spectral/$hp$ Element Methods" delivers what the title implies: using a high-fidelity, large-eddy simulation (LES) technology that is based on spectral/$hp$ element methods, the group of eight authors demonstrates in this article how it is possible to simulate performance of an Elemental Rp1 road car. Given the high Reynolds numbers and complex geometry involved, the authors carefully address both the creation of highly accurate meshes while also producing “physically faithful" results in reasonable time. To this end, one section is devoted to the high-order meshing strategy that is used to prevent unphysical diffusion. A separate section on the numerical methods describes the regularization approach the authors use to treat underresolved scales, the de-aliasing strategies employed, and how to use parallelization and preconditioned iterative solvers to address the need for computational efficiency. Colorful and detailed illustrations accompany the simulation studies in section 4, allowing the reader to visually assess the impact of the proposed approach. In short, the authors propose a comprehensive strategy that allows methods that were developed within the academic community along with new innovations to be translated into the space of an industrial CFD application for substantial gain. Their success may inspire other researchers to follow this road in the future. Readers, start your engines! Finite-volume methods for discretization of fluid flow are called supraconservative if, besides preserving primary invariants (e.g., those invariants pertaining to primary variables from the constituting conservation laws), they also preserve secondary (i.e., other) invariants. A finite-volume method having this property ensures better discrete equivalence among the discretizations of the analytically equivalent formulations of the model. The RS paper “Supraconservative Finite-Volume Methods for the Euler Equations of Subsonic Compressible Flow," authored by Arthur E. P. Veldman and presented in this issue, is concerned with the construction of such finite-volume methods. The starting point is the analytic formulation in (1), and the goal is the secondary conservation of energy in the finite-volume method. According to the author, there is a feature that sets the present approach apart from most of the discretization approaches covered in the extensive literature review contained herein: after discretizing (1.1) in such a way as to ensure the discrete conservation of the primary invariants, the author does not return to the analytical formulation but rather uses the “freedom left in the [discrete level] formulation" to generate the secondary invariants. The paper provides the details for a supraconservative method for incompressible flow on two grid types: (1) structured, staggered and (2) unstructured, collocated. The author leaves readers to consider a few open questions, such as whether “their favorite discretization approach can be made to satisfy [the] requirements" given here that would allow them to view their method through a similar lens.

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研究焦点

SIAM 评论，第 63 卷，第 4 期，第 721-721 页，2021 年 1 月。
本期 SIAM 评论中以汽车为主题的封面艺术由本期两篇研究聚焦文章中的第一篇提供。事实上，论文“通过光谱/$hp$ 元素方法对高性能公路车进行工业相关隐式大涡模拟”提供了标题所暗示的内容：使用高保真大涡模拟 (LES) 技术，基于光谱/$hp$ 元素方法，由八位作者组成的小组在本文中展示了如何模拟 Elemental Rp1 公路车的性能。鉴于涉及的高雷诺数和复杂的几何形状，作者仔细地解决了这两个问题创建高度精确的网格，同时在合理的时间内产生“物理上忠实”的结果。为此，一节专门介绍用于防止非物理扩散的高阶网格划分策略。关于数值方法的单独部分描述了作者用于处理未充分解析尺度的正则化方法、所采用的去混叠策略，以及如何使用并行化和预处理迭代求解器来满足计算效率的需求。第 4 节中的模拟研究附有彩色和详细的插图，使读者能够直观地评估所提议方法的影响。简而言之，作者提出了一个综合策略，允许将学术界内开发的方法以及新的创新转化为工业 CFD 应用程序空间，以获得实质性收益。他们的成功可能会激励其他研究人员在未来走这条路。读者们，启动你们的引擎吧！用于流体流动离散化的有限体积方法被称为超保守，如果除了保留主要不变量（例如，与构成守恒定律中的主要变量有关的那些不变量），它们还保留次要（即，其他）不变量。具有此属性的有限体积方法可确保模型的解析等效公式的离散化之间具有更好的离散等效性。RS 论文“用于亚音速可压缩流的欧拉方程的超保守有限体积方法”由 Arthur EP Veldman 撰写并在本期中介绍，该论文涉及此类有限体积方法的构建。起点是(1), 目标是有限体积法中的二次能量守恒。根据作者的说法，有一个特征使本方法与本文包含的广泛文献综述中涵盖的大多数离散化方法不同：在以确保主要不变量的离散守恒的方式对（1.1）进行离散化之后，作者没有回到解析公式，而是使用“[离散水平]公式中的自由度”来生成二次不变量。本文提供了两种网格类型上不可压缩流动的超保守方法的详细信息：（1）结构化、交错和 (2) 非结构化、搭配。作者让读者考虑一些开放性问题，