双曲型守恒律的一种五阶半离散中心迎风格式  

A Fifth-order Semi-discrete Central-upwind Scheme for Hyperbolic Conservation Laws

作　　者：胡彦梅[1] 陈建忠[2] 封建湖[1] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]西北工业大学,陕西西安710072

出　　处：《计算物理》2008年第1期29-35,共7页Chinese Journal of Computational Physics

摘　　要：给出一种求解双曲型守恒律的五阶半离散中心迎风格式.对一维问题,该格式以五阶中心WENO重构为基础;对二维问题,用逐维计算的方法将五阶中心WENO重构进行推广.时间方向的离散采用Runge-Kutta方法.格式保持了中心差分格式简单的优点,即不用求解Riemann问题,避免进行特征分解.用该格式对一维和二维Euler方程进行数值试验,结果表明该格式是高精度、高分辨率的.A fifth-order semi-discrete central-upwind scheme for hyperbolic conservation laws is proposed. In one dimension, the scheme is based on a fifth-order central weighted essentially non-oscillatory（WENO） reconstruction： In two dimensions, the reconstruction is generalized by a dimension-by-dimension approach. A Runge-Kutta method is employed in time integration. The method requires neither Riemann solvers nor characteristic decomposition and therefore enjoys main advantage of the central schemes. The present scheme is verified by one and two dimensional Euler equations of gas dynamics and shows high resolution and high accuracy.

关 键 词：双曲型守恒律 中心迎风差分格式 半离散 中心WENO重构 

分 类 号：O35[理学—流体力学] O241.82[理学—力学]