基于NAD算子的三阶Runge-Kutta方法及波场模拟  

Third order Runge-Kutta method and wave field simulation based on NAD operator

作　　者：陈丽 张朝元 朱兴文 李梦巧 CHEN Li;ZHANG Chaoyuan;ZHU Xingwen;LI Mengqiao(College of Engineering,Dali University,Dali 671003,China;College of Mathematics and Computer,Dali University,Dali 671003,China)

机构地区：[1]大理大学工程学院,云南大理671003 [2]大理大学数学与计算机学院,云南大理671003

出　　处：《成都理工大学学报（自然科学版）》2023年第1期122-128,共7页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：国家自然科学基金项目(41664005,41464004,51809026);云南省地方本科高校(部分)基础研究联合专项资金项目(202001BA070001-082,2017FH001-006);大理大学科研发展基金项目(FZ2023YB035,FZ2023YB039)。

摘　　要：为求解二维声波方程,本文结合空间高阶偏导数离散化的八阶NAD算子和时间导数离散化的三阶Runge-Kutta方法,推导出八阶NAD-RK算法。详细研究了八阶NAD-RK算法的计算效率和地震波数值模拟。结果显示:在达到相同精度下,八阶NAD-RK算法的内存需求约为八阶LWC算法的20%,约为八阶SG算法的25%;八阶NAD-RK算法的计算速度约为八阶LWC算法的5.8倍,约为八阶SG算法的1.52倍。地震波数值模拟实验进一步验证八阶NAD-RK算法数值频散压制效果。By combining the eighth-order NAD operator of the higher-order partial derivative discretization in space with the third-order Runge-Kutta discretization of the time derivative,the eighth-order NAD-RK algorithm is derived to solve the two-dimensional acoustic wave equation.Then,the computational efficiency of eighth order NAD-RK algorithm and seismic wave numerical simulation are studied.The results show that the memory requirement of the eighth-order NAD-RK algorithm is about 20%of that of the eighth-order LWC algorithm and about 25%of that of the eighth-order SG algorithm with the same accuracy.The computational speed of the eighth-order NAD-RK algorithm is about 5.8 times that of the eighth-order LWC algorithm and about 1.52 times that of the eighth-order SG algorithm.The numerical simulation experiment of seismic wave has further verified the numerical dispersion suppression effect of eighth-order NAD-RK algorithm.

关 键 词：声波方程 NAD算子 RUNGE-KUTTA方法 计算效率 数值模拟 

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