用于线性波动方程的高精度显式差分算法性能分析  

Analysis of High Order Explicit Finite Difference Schemes for Linear Wave Equations

作　　者：罗柏华[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海大学学报（自然科学版）》2006年第3期278-282,287,共6页Journal of Shanghai University:Natural Science Edition

摘　　要：研究了一类低耗散、低色散的高阶精度显式有限差分方法,目的是直接计算非定常的线性波动问题.空间离散采用DRP类的七点四阶精度优化中心差分格式,给出了两种降低色散误差的优化方法;时间积分用四阶精度龙格库塔方法(RK4和LDDRK).分析比较了3种空间离散格式的有效波数范围、各种全离散格式的耗散和色散误差特性、波的长距离传播计算时格式的累积误差特性,对这类格式的运用提出了建议.A type of low-dissipation and low-dispersion high-order finite difference scheme is studied for computation of wave motion. An optimized seven-point central difference is used to approximate the spatial derivative, and two optimization methods are presented. For the time marching, the fourth order explicit Runge-Kutta methods （RK4 and LDDRK） are used. All effective wave-number ranges of the three spatial schemes, numerical errors of various full schemes, and minimum point numbers per wavelength （ppw） for long distance wave propagation calculation are studied. Based on the comparison, suggestions on the use of these schemes are given.

关 键 词：有限差分 计算气动声学 高精度 

分 类 号：O422[理学—声学] V211.3[理学—物理]