五阶FD-WENO格式和二阶Godunov格式MUSCL的数值测试与定量比较  

Numerical Comparison of Fifth-order WENO Schemes and Second-order Godunov Schemes

作　　者：杨水平[1] 李寿佛[1] 屈小妹[1] 张瑗[1] 刘玉珍[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2006年第2期8-12,共5页Natural Science Journal of Xiangtan University

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

摘　　要：研制了用5阶FD-WENO格式(WENO5)及2阶Godunov格式(MUSCL)求解双曲守恒律组的应用软件.通过求解若干Riemann问题及较复杂的一维激波相互碰撞问题对这些软件进行测试和定量比较,发现对于Sod Riemann问题,两种格式都易于算出具有较高精度和较高分辨率的数值结果.The software for solving the hyperbolic eonservation laws with Fifth - order FD WENO schemes （WENOS） and second- order Godunov schemes （MUSCL） are developed. To lest and compare the softwares, computations on some Riemann problems anti one- dimensional complex interacting blast wave problem are carried nut. Numerical results show that for the Sod Riemann problem, high accuracy and high resolution results arc easily achieved by both schemes, WE- NO5 has small viscosity, MUSCL has some small local oscillatinn obviously. But for the Woodward- Cnlella interacting blast wave problem and Peak Riemann problem and WENO5 is obviously better than MUSCL around the shock and the rarefaction, and WENO5 ant only has a higher resolution but also smaller ernst.

关 键 词：WENO格式 Godunov格式 双曲守恒律组 

分 类 号：O241.82[理学—计算数学] O351.3[理学—数学]