用于波动方程计算的高阶精度紧致差分方法  

High Order Compact 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）》2009年第2期134-141,共8页Journal of Shanghai University:Natural Science Edition

摘　　要：研究低耗散低色散的高阶精度紧致差分方法,目的是直接模拟非定常的波动问题。空间导数采用七点六阶以上精度的紧致差分逼近,研究3种空间离散格式:一个通过降低色散(相位)误差得到优化格式CO6,以及标准的五点六阶紧致格式C6和七点八阶精度紧致格式C8;时间推进采用2种四阶精度的Runge-Kutta方法(RK4和RK46)。分析比较空间离散格式的有效波数范围、空间-时间全离散格式的误差特性、长距离波传播计算时的累积误差特性。通过对全离散格式的误差等特性的分析比较,对这类格式的应用提出建议。最后,通过流体波动问题算例,验证了该格式计算波动问题的高精度特性。Low-dissipation and low-dispersion high-order compact finite difference schemes are studied for computation of wave motion. An optimized seven-point sixth order accurate compact finite difference scheme （C06） is obtained to approximate spatial derivatives, and is compared with the C6 （sixth-order compact） and C8 （eighth-order compact） schemes. For time marching scheme, the fourth order explicit Runge-Kutta methods （RK4 and LDDRK or RK46） are used. The effective wave-number ranges of the spatial schemes, the numerical errors of the various schemes, and the minimum point numbers per wavelength （ppw） for long distance propagation calculation of waves are studied. Based on the comparison, suggestions are given in using these schemes. Finally, a few numerical tests are presented to show accuracy of the schemes in simulation of wave motion.

关 键 词：紧致差分格式 计算气动声学 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] O422[理学—声学]