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力学进展 ›› 2013, Vol. 43 ›› Issue (6): 541-554.doi: 10.6052/1000-0992-13-059

• 论文 •    下一篇

计算流体力学中的间断Galerkin方法述评

舒其望   

  1. Division of Applied Mathematics Brown University Providence, RI 02912, USA
  • 收稿日期:2013-08-27 出版日期:2013-11-25 发布日期:2013-12-02
  • 通讯作者: 舒其望 E-mail:shu@dam.brown.edu

A brief survey on discontinuous Galerkin methods in computational fluid dynamics

Chi-Wang Shu   

  1. Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
  • Received:2013-08-27 Online:2013-11-25 Published:2013-12-02
  • Contact: O35 E-mail:shu@dam.brown.edu
  • Supported by:

    The project was partially supported by US NSF grant DMS-1112700 and by the Open Fund of State Key Laboratory of High-temperature Gas Dynamics, China (No. 2011KF02).

摘要:

间断Galerkin (DG)方法结合了有限元法(具有弱形式、有限维解和试验函数空间)和有限体积法(具有数值通量、非线性限制器)的优点,特别适合对流占优问题(如激波等线性和非线性波)的模拟研究,本文述评DG 方法,强调其在计算流体力学(CFD)中的应用,文中讨论了DG 方法的必要构成要素和性能特点,并介绍了该方法的一些最近研究进展,相关工作促进了DG 方法在CFD 领域的应用,

关键词:

间断Galerkin(DG)方法|计算流体力学

Abstract:

Discontinuous Galerkin (DG) methods combine features in finite element methods(weak formulation, finite dimensional solution and test function spaces) and in finite volume methods (numerical fluxes, nonlinear limiters) and are particularly suitable for simulating convection dominated problems, such as linear and nonlinear waves including shock waves. In this article we will give a brief survey of DG methods, emphasizing their applications in computational fluid dynamics (CFD). We will discuss essential ingredients and properties of DG methods, and will also give a few examples of recent developments of DG methods which have facilitated their applications in CFD.

Key words:

discontinuous Galerkin methods|computational fluid dynamics

中图分类号: 

  • O35