2类高阶格式数值测试和比较  

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

作　　者：杨水平[1] 李寿佛[2] 莫宏敏[3] 

机构地区：[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　　处：《吉首大学学报（自然科学版）》2007年第4期30-34,共5页Journal of Jishou University(Natural Sciences Edition)

基　　金：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

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Ray-leigh-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.A numerical study is undertaken to compare the fifth-order finite difference weighted essentially non-oscillatory scheme （FD-WEN05） 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.

关 键 词：WENO格式 Godunov格式 EULER方程 

分 类 号：O241.82[理学—计算数学] O351.3[理学—数学]