欧拉和纳维-斯托克斯方程空间高阶精确离散化的时间推进格式

IF 11.5 1区 工程技术 Q1 ENGINEERING, AEROSPACE Progress in Aerospace Sciences Pub Date : 2022-04-01 DOI:10.1016/j.paerosci.2021.100795
Yongle Du , John A. Ekaterinaris
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引用次数: 0

摘要

计算流体动力学(CFD)方法用于Euler和Navier-Stokes方程的数值解已经足够成熟,并且能够在流体动力学研究和工程应用中进行高保真度的模拟。本文首先对目前仍在广泛使用的低阶(二阶或更低)精确的时空离散化格式进行了综述,以说明高阶数值格式以及稳定性和误差分析技术的优点。然后,讨论了流行的高阶空间离散化方案,强调了它们对高阶隐式时间推进的好处和挑战。在此之后,我们将重点放在隐式时间推进的主要方面,结合龙格-库塔方法和高阶空间离散化,已被证明可以有效地解决非定常流动。除了构造高阶隐式龙格-库塔格式外,还详细讨论了多物理流现象中关于增强非线性稳定性和低色散低耗散误差的最新进展。综述了先进高性能计算机上隐式并行解的有效求解技术,如基于近似分解的传统LU-SGS法和ADI法、带子迭代的牛顿迭代法等。作为另一个具有挑战性的问题,隐式边界条件的执行也得到了阐述,我们特别关注最近的发展及其在计算效率和准确性方面提供的好处。
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Time-marching schemes for spatially high order accurate discretizations of the Euler and Navier–Stokes equations

Computational fluid dynamics (CFD) methods used for the numerical solution of the Euler and Navier–Stokes equations have been sufficiently matured and enable to perform high fidelity simulations in fluid dynamics research and engineering applications. In this review, some low-order (second order or lower) accurate space–time-domain discretization schemes that are still widely in use are reviewed first, in order to show the benefits of high order numerical schemes and the techniques for stability and error analysis. Then, popular high order spatial discretization schemes are discussed to highlight the benefits and also the challenges they impose on high order implicit time advancement. After these, we focus on the major aspects of implicit time advancement combining the Runge–Kutta methods and high order spatial discretizations that have been proven efficient to resolve unsteady flows. In addition to the construction of high order implicit Runge–Kutta schemes, more recent development concerning enhanced nonlinear stability and low-dispersion low-dissipation errors is discussed in detail for multi-physical flow phenomena. Efficient solution techniques for implicit parallel solutions on advanced high-performance computers are reviewed, such as the traditional LU-SGS and ADI methods based on the approximate factorization, the Newton iterative method with subsidiary iterations, etc. As another challenging issue, enforcement of implicit boundary conditions is also elaborated, and we focus especially on the recent developments and the benefits they offer regarding computational efficiency and accuracy.

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来源期刊
Progress in Aerospace Sciences
Progress in Aerospace Sciences 工程技术-工程:宇航
CiteScore
20.20
自引率
3.10%
发文量
41
审稿时长
5 months
期刊介绍: "Progress in Aerospace Sciences" is a prestigious international review journal focusing on research in aerospace sciences and its applications in research organizations, industry, and universities. The journal aims to appeal to a wide range of readers and provide valuable information. The primary content of the journal consists of specially commissioned review articles. These articles serve to collate the latest advancements in the expansive field of aerospace sciences. Unlike other journals, there are no restrictions on the length of papers. Authors are encouraged to furnish specialist readers with a clear and concise summary of recent work, while also providing enough detail for general aerospace readers to stay updated on developments in fields beyond their own expertise.
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