一个基于通量分裂的高精度MmB差分格式  

A high order accurate MmB difference scheme based on flux splitting

作　　者：郑华盛[1] 赵宁[1] 

机构地区：[1]南京航空航天大学空气动力学系

出　　处：《空气动力学学报》2005年第1期52-56,20,共6页Acta Aerodynamica Sinica

基　　金：航空科学基金项目 (0 1A52 0 0 3 ;0 2A52 0 0 4 );国防预研项目资助

摘　　要：本文研究双曲型守恒律的高精度差分方法。在新的算法中 ,首先将计算区间划分为互不相交的小区间 ,再根据精度要求等分小区间 ;其次 ,根据流动方向进行通量分裂 ,重构小区间交界面上的正、负数值通量 ,并进行校正 ;然后 ,采用高阶Runge KuttaTVD方法进行时间离散 ,构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的守恒型差分格式。推广到二维双曲型守恒律方程 ,证明了格式的MmB特性。进而推广到二维守恒型方程组情形。最后对二维Burgers方程及Euler方程进行了数值试验 。In this paper, a high order accurate difference scheme is presented for nonlinear hyperbolic conservation laws. Firstly, the computational domain is divided into many pieces of non-overlapping subdomains, and then each subdomain is further subdivided into equal small-cells according to required accuracy. Secondly, by the flow direction, fluxsplitting will be used, and the positive/negative numerical fluxes are reconstructed at small-cell boundaries, and the correction are introduced. With the aid of high-order TVD Runge-Kutta time discretization, a high-order ,high resolution, conservative difference scheme is constructed for one dimensional nonlinear hyperbolic conservation laws . The scheme is extended to two dimensional hyperbolic conservation equation by dimension-by-dimension method, and the MmB property of the scheme is proved. Furthermore, The extension to two dimensional system of conservation laws is carried out. Finally , several numerical experiments on two dimensional Euler equations are given, and numerical results are satisfied.

关 键 词：双曲型 守恒律 差分格式 时间离散 通量 二维 BURGERS方程 数值试验 高分辨率 高精度 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程] O175.27[理学—数学]