摘要
基于二维声波方程,本文首先采用四级四阶的Runge-Kutta方法对时间导数进行四阶离散,而利用近似解析离散化方法对空间高阶偏导数进行八阶离散,从而得到了八阶NAD-RK方法.然后,从理论上和数值模拟上对该方法进行了数值频散分析,并与八阶LWC方法和八阶SG方法进行了比较.结果揭示,八阶NAD-RK方法有着很好压制数值频散和提高模拟精度等优点.
In this paper,we firstly gain the eighth-order NAD-RK method based on the 2-D acoustic wave equation.This method uses the fourth-order Runge-Kutta method to conduct fourth-order discretization on temporal derivatives,and employs the nearly analytic discretization method to conduct eighth-order discretiza-tion on high order partial derivatives of the space.Secondly,the numerical dispersion of this method is analyzed from the theory and numerical simulation.The paper finally compares the method with the eighth-order Lax-Wendroff correction （LWC）and the eighth-order staggered-grid （SG）methods.These results show that the eighth-order NAD-RK method can suppress numerical dispersion and enhance computational simulation accu-racy.
出处
《昆明理工大学学报（自然科学版）》
CAS
北大核心
2014年第2期113-119,共7页
Journal of Kunming University of Science and Technology(Natural Science)
基金
云南省教育厅科学研究基金重点项目(2013Z152)
云南省教育厅科学研究基金一般项目(2010C140)
云南省教育厅科学研究基金一般项目(2011C123)
大理学院教改项目(JGⅣ-46)
关键词
声波方程
近似解析离散化
四阶Runge-Kutta方法
数值频散
波场模拟
acoustic wave equation
nearly analytic discretization
fourth -order Runge -Kutta method
nu-merical dispersion
wave-field simulation
