2类高阶格式数值测试和比较

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

2类高阶格式数值测试和比较

（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.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/Abstract

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

杨水平, 李寿佛, 莫宏敏. 2类高阶格式数值测试和比较[J]. journal6, 2007, 28(4): 30-34.

YANG Shui-Ping, LI Shou-Fu, MO Hong-Min. Numerical Study of Two High-Order Schemes for Compressible Euler Equation[J]. journal6, 2007, 28(4): 30-34.

参考文献

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[5] BALSARA D,SHU C W.Monotonicity Preserving Weighted Essentially Non-Oscillatory Schemes with Increasingly High Order of Accuracy [J].J. Com. Phys.,2001,160:405-45.

[6] SHU C W.Essentially Non-Oscillatory Schemes and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws [A].COCKBURN B,JOHNSON C,SHU C W,et al.Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Lecture Notes in Mathematics [C].Springer,1998,1 697:325-432.

[7] JIANG G，SHU C W.Efficient Implementation of Weighted ENO Schemes [J].J. Com. Phys.,1996，126:202-228.

[8] COLELLA P，WOODAWARD P R.The Piecewise Parabolic Method(PPM) for Gas-Dynamics Simulations [J].J. Com. Phys.,1984,54:174.

[9] HARTEN A,OSHER S.Uniformly High Order Accurate Essentially Non-Oscillatory Scheme [J].I SIAM J. Numer. Ana.,1987,24:279-309.

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