journal6 ›› 2007, Vol. 28 ›› Issue (4): 30-34.

• 数学 • 上一篇    下一篇

2类高阶格式数值测试和比较

  

  1. (1.惠州学院数学系,广东 惠州 516007;2.湘潭大学数学与计算科学学院,湖南 湘潭 411105;3.吉首大学数学与计算机科学学院,湖南 吉首 416000)
  • 出版日期:2007-07-25 发布日期:2012-06-15
  • 作者简介:杨水平(1982-),男,湖南芷江人,硕士研究生,主要从事计算流体力学研究.
  • 基金资助:

    国家自然科学基金资助项目(10271100);国家863高技术惯性约束聚变主题资助项目

Numerical Study of Two High-Order Schemes for Compressible Euler Equation

  1. (1.Mathematics Department,Huizhou University,Huizhou 516007,Guangdong China;2.College of Mathematics and Computation Science,Xiangtan University,Xiangtan 411105,Hunan China;3.College of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China)
  • Online:2007-07-25 Published:2012-06-15

摘要:通过求解二维Burgers方程初边值问题、二维周期漩涡问题、Richtmyer Meshkov(简称RM)不稳定性问题和Rayleigh-Taylor(简称RT)不稳定性问题,对五阶FD-WENO格式(简称WENO5)及二阶Godunov格式MUSCL进行了数值测试和比较.所得结果对于求解气体动力学问题及辐射流体力学问题时,怎样恰当地选择数值方法具有一定参考作用.

关键词: WENO格式, Godunov格式, Euler方程

Abstract: A numerical study is undertaken to compare the fifth-order finite difference weighted essentially non-oscillatory scheme (FD-WENO5) to the second-order Godunov scheme  MUSCL (monotonic upstream-centered scheme for conservation laws).For quantitative comparison purpose,these methods are tested on a series of problems whose true solutions are known or can be computed with high accuracy,such as the two-dimensional Burgers initial problems,the two-dimensional periodic vortex problem,Richtmyer-Meshkov instability problems and Rayleigh-Taylor instability problems.The results can be referred to as to how to choose the numerical method when solving the problems of gas dynamics and radiation hydrodynamics.

Key words: weighted essentially non-oscillatory scheme, Godunov scheme, Euler equation

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