A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows

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• 作者：Naveed Ahmed ; Tomás Chacón Rebollo…
• 刊名：Archives of Computational Methods in Engineering
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：24
• 期：1
• 页码：115-164
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Appl.Mathematics/Computational Methods of Engineering;
• 出版者：Springer Netherlands
• ISSN：1886-1784
• 卷排序：24

文摘

Various realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: they are based on the variational formulation of the incompressible Navier–Stokes equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this review, the derivation of the different VMS methods is presented in some detail and their relation among each other and also to other discretizations is discussed. Another emphasis consists in giving an overview about known results from the numerical analysis of the VMS methods. A few results are presented in detail to highlight the used mathematical tools. Furthermore, the literature presenting numerical studies with the VMS methods is surveyed and the obtained results are summarized.