双曲型守恒律的一类局部化的高效差分格式  

A Class of Localized High Resolution Difference Schemes for Hyperbolic Conservation Laws

作　　者：郑华盛[1] 李曦[1] 胡结梅[1] 

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《西南师范大学学报（自然科学版）》2010年第2期58-63,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：江西省教育厅2008年度科技项目计划(GJJ08224);江西省自然科学基金(0611096);南昌航空大学博士启动基金(EA20060731)资助项目

摘　　要：构造了一维非线性双曲型守恒律的一类局部化的高效全离散差分格式,并将该格式推广到一维守恒方程组及二维守恒方程(组).最后,给出了几个标准算例.数值计算结果表明此格式具有高精度高分辨激波、稀疏波和接触间断,且边界条件易于处理等优点.In this paper, a class of localized high-resolution fully discretization difference schemes is presented for one dimensional nonlinear hyperbolic conservation laws. And then the scheme is extended to solve one dimensional and two dimensional hyperbolic conservation laws and system. Finally, several typical numerical experiments on Euler equations are given. The numerical results show that these schemes have the advantages of high-order accuracy and high resolution of shock, rarefaction wave and contact discontinuity and easy to treat boundary conditions.

关 键 词：双曲型守恒律 高阶精度 离散GDQ方法 TVB格式 Runge—Kutta TVD时间离散 

分 类 号：O241.8[理学—计算数学] V211.3[理学—数学]