一种弱数值频散的四阶Runge-Kutta方法及二维声波场模拟  

The four-order Runge-Kutta method with weak numerical dispersion and acoustic wave-field simulation of two-dimension

作　　者：张朝元[1,2] 宋国杰[3] 

机构地区：[1]大理学院数学与计算机学院,云南大理671003 [2]清华大学数学科学系,北京100084 [3]清华大学计算机系,北京100084

出　　处：《云南大学学报（自然科学版）》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)

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.

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 

分 类 号：P631[天文地球—地质矿产勘探] O241[天文地球—地质学]