一个基于通量分裂的高精度MmB差分格式

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-Kutta TVD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,数值结果令人满意.

A high order accurate MmB difference scheme based on flux splitting

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.