八阶NAD-RK方法及其数值频散研究  

The Eighth-order NAD-RK Method and Its Numerical Dispersion Research

作　　者：陈丽 张朝元 Chen Li;Zhang Chaoyuan(College of Engineering,Dali University,Dali 671003,Yunnan,China;College of Mathematics and Computer,Dali University,Dali 671003,Yunnan,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：《科技通报》2023年第4期10-14,共5页Bulletin of Science and Technology

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方法。详细推导和分析了八阶NAD-RK方法的数值频散。结果显示:同八阶Lax-Wendroff(LWC)格式和八阶交错网格(SG)格式相比,八阶NAD-RK方法具有最小的数值频散和最小的数值频散各向异性。该方法能够有效地抑制粗网格条件下声波方程离散化引起的数值频散。For solving the 2-D acoustic wave equation,an eighth-order NAD-RK method is derived by combining the eighth-order NAD operator to discretize the high-order partial derivatives of space directions with the third-order Runge-Kutta method to discretize the high-order partial derivatives of temporal directions.The numerical dispersion of the eighth-order NAD-RK method is derived and analyzed in detail.Results show that compared with the eighth-order Lax-Wendroff(LWC)method and the eighthorder staggered grid(SG)method,the eighth-order NAD-RK method has the minimum numerical dispersion and the minimum numerical dispersion anisotropy.And,the new method is effective to suppress the numerical dispersion caused by discretizing the acoustic wave equation when too coarse grids are used.

关 键 词：声波方程 NAD算子 RUNGE-KUTTA方法 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]