摘要
针对二维声波方程,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,并采用四阶Runge-Kutta方法对时间导数进行四阶离散,得到了八阶NAD-RK方法.将该方法应用于双层介质模型和三层介质模型中进行波场数值模拟,同时与八阶LWC方法和八阶SG方法进行了比较.结果表明,八阶NAD-RK方法具有弱数值频散和高计算模拟效果等优势.
We gain the eight - order NAD - RK method based on the acoustic wave equation of two - dimen sion. This method uses the nearly analytic diseretization method to conduct eight - order discretization on high or der partial derivatives of the space, and employs the four - order Runge - Kutta method to conduct four - order discretization on temporal derivatives. The method is applied to wave - field numerical simulations from the two layer acoustic and three - layer acoustic models in the 2 - D case. The paper compares the method against the eighth - order LAX - Wendroff correction （ LWC ） and the eighth - order staggered - grid （SG） finite - differ ence methods. These results illustrate that the eight - order NAD - RK method has advantages such as weak nu merical dispersion and high computational simulation effect.
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第6期731-737,共7页
Journal of Yunnan University(Natural Sciences Edition)
基金
国家自然科学基金(41204074)
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(2010C140)
关键词
声波方程
近似解析离散化
四阶Runge-Kutta方法
波场模拟
数值频散
acoustic wave equation
nearly analytic discretization
four - order Runge - Kutta method
wavefield simulation
numerical dispersion
作者简介
张朝元（1978-），男，湖南人，讲师，主要研究方向为地震波方程的数值方法及波场模拟．E-mail：zcy-km@163.com.
