求解波动方程的准粒子离散修正辛算法

Modified symplectic quasi-particles discrete methods for simulation of wave propogation

针对波动方程求解,在Hamilton体系下建立了对空间离散的准粒子体系,该准粒子体系实现简单,物理意义明确;在时间离散方面,构造了一种适合高效声波模拟的修正辛格式,该格式是在常规的二阶Partitioned Runge-Kutta（PRK）基础之上构造而成,其具有三阶时间精度,从理论上分析了修正辛格式的数值稳定性和频散性能.数值结果表明,本文提出的方法在计算时间,计算精度和计算存储量等各方面性能都有相应改善。

Hamiltonian system with quasi-particles for spatial discrete of acoustic wave propogation is presented. A modified symplectic scheme for temporal discretization of wave equation is proposed. First, we transformed the wave equation into a Hamilton system. An explicit symplecitc Partitioned Runge-Kutta （PRK） scheme is used to solve the Hamilton system. Then, the additional spatial discretization term is added into the symplectic PRK scheme. Theoretical analytic shows the new scheme has lower dispersion and long-term calculation ability than that of the conventional symplectic schemes. Numerical results indicate that the present method is effective and feasible, such as the low numerical dispersion, high stability and long-time performance of the new scheme.