低耗散低色散有限差分格式误差分析

基于7点中心色散保持(DRP)空间离散格式,结合5种龙格库塔(RK)时间积分方法,从误差构成、误差传播、误差累积3个角度出发,采用传统Von Neumann误差分析方法和修正误差传播分析方法,分析比较了各时间离散格式和全离散格式的耗散色散误差,波数分辨能力,长距离波计算误差传播,低频波、中频波、高频波的误差累积特性,还从稳定性、求解精度等角度分析比较了各组合格式的优劣,获得了与7点中心DRP格式组合的最佳时间离散格式ORK6;最后对一维标量和矢量波动问题计算验证了各组合格式的准确模拟能力.

Error Analysis of Low Dissipation and Low Dispersion Finite Difference Schemes

Based on the seven point central dispersion relation preserving(DRP) space discretization scheme,and combined with five kinds of Runge-Kutta time integration scheme,the dissipation and dispersion errors induced by time and global discretization schemes,the effective wave number ranges,the error propagation of long distance,the accumulated error of low,middle and high frequency wave were analyzed by using traditional Von Neumann method and a new correct error propagation method from three aspects,i.e.,error component,error propagation,and error accumulation.In addition,the advantage and disadvantage of all the combined schemes were compared by analyzing their stability and accuracy.The accuracy of ORK6 time integration scheme combined with seven point central space discretization scheme was the highest among these combination schemes.Finally,a few numerical tests were presented to show the accuracy of these schemes in simulation of one dimensional scalar and vector wave motion.