求解声波方程的辛RKN格式  

Symplectic RKN schemes for seismic scalar wave simulations

作　　者：刘少林[1,2] 李小凡[1] 刘有山[1,2] 陈世仲[1,2] 

机构地区：[1]中国科学院地质与地球物理研究所中国科学院地球深部研究重点实验室,北京100029 [2]中国科学院大学,北京100049

出　　处：《地球物理学报》2013年第12期4197-4205,共9页Chinese Journal of Geophysics

基　　金：国家自然科学基金(41174047;40874024)资助

摘　　要：将声波方程变换至Hamiltion体系,构造了适用于高效声波模拟的二阶显式辛Runge-Kutta-Nystrm(RKN)格式,运用根数理论得到此格式的阶条件方程组.针对两个自由度的辛条件方程组,根据三次项截断误差最小原理得到一种误差最小辛格式;通过分析声波的时间演进方程的稳定性,选择不同的辛系数使演进方程更稳定,并得到了另一种更为稳定辛格式;在频散关系分析中,选择使数值频散最小的辛系数,得到第三种最小频散辛格式.在理论分析中,这组辛RKN格式相比常见格式在精度控制、数值频散压制以及稳定性提升等方面均具有明显优势;在数值实验中,通过具体算例验证了理论分析的正确性.In this paper, seismic scalar wave equation is transformed into Hamiltonian system, a second-order explicit Runge-Kutta-Nystrom （RKN） scheme is proposed for high-efficient acoustic wave simulations. The order conditions are obtained by the rooted trees theory. For order conditions with two free coefficients, a minimum error scheme is obtained based on the minimum error truncations in the third order terms. We analyze the acoustic time advancing equation and choose coefficients to promote the stability limit, and then we develop optimized stable scheme. In dispersion relation analysis, the third optimal symplectic RKN scheme is constructed to substantially eliminate numerical dispersion. The theoretical properties of this set of symplectic RKN schemes possess greater power than other common schemes in terms of errors controlling, numerical dispersion suppressing and stability promoting. Finally, we present numerical results to verify the theoretical analysis.

关 键 词：声波波场 辛RKN格式 截断误差 稳定性 频散关系 

分 类 号：P631[天文地球—地质矿产勘探]