The High-Precision Runge-Kutta Method for Solving Two-Dimensional Acoustic Wave Equation

Abstract

Abstract:

Based on the two-dimensional acoustic wave equation， the eighth-order NAD-RK algorithm is developed by combining the higher order partial derivative of the discrete space of the eighth-order NAD operator and the discrete time derivative of the third-order Runge-Kutta method. The theoretical and numerical errors of the eighth-order NAD-RK algorithm are analyzed， and its stability conditions are derived in detail. The results show that compared with the eighth-order Lax-Wendroff scheme and the eighth-order staggered grid scheme， the eighth-order NAD-RK algorithm has the smallest numerical error.

Key words:

"> acoustic wave equation">, NAD operator">, Runge-Kutta method">, error analysis">, stability condition

CLC Number:

Chen Li, Zhu Xingwen, Zhang Chaoyuan.

The High-Precision Runge-Kutta Method for Solving Two-Dimensional Acoustic Wave Equation [J]. Journal of Dali University, 2023, 8(6): 20-23.

References

〔1〕 DABLAIN M A. The Application of High-Order Differencing to Scalar Wave Equation〔J〕. Geophysics， 1986， 51（1）： 54-66.

〔2〕 YANG D H， LIU E， ZHANG Z J， et al. Finite-Difference Modelling in Two-Dimensional Anisotropic Media Using a Flux-Corrected Transport Technique〔J〕. Geophysical Journal International， 2002， 148（2）： 320-328.

〔3〕杨顶辉. 双相各向异性介质中弹性波方程的有限元解法及波场模拟〔J〕. 地球物理学报， 2002， 45（4）： 575-583.

〔4〕孙耿. 波动方程的一类显式辛格式〔J〕. 计算数学， 1997， 19（1）： 1-10.

〔5〕董良国，马在田，曹景忠，等. 一阶弹性波方程交错网格高阶差分解法〔J〕. 地球物理学报，2000，43（3）：411-419.

〔6〕 YANG D H， TENG J W， ZHANG Z J， et al. A Nearly-Analytic Discrete Algorithm for Acoustic and Elastic Wave Equations in Anisotropic Media〔J〕. Bulletin of the Seis-mological Society of America， 2003， 93（2）： 882-890.

〔7〕 CHEN S， YANG D H， DENG X Y. A Weighted Runge-Kutta Method with Weak Numerical Dispersion for Solving Wave Equations〔J〕. Communications in Computational Physics， 2010， 7（5）： 1027-1048.

〔8〕王磊，杨顶辉，邓小英. 非均匀介质中地震波应力场的WNAD方法及其数值模拟〔J〕. 地球物理学报， 2009， 52（6）： 1526-1535.

〔9〕 YANG D H， SONG G J， CHEN S， et al. An Improved Nearly Analytical Discrete Algorithm： An Efficient Tool to Simulate the Seismic Response of 2-D Porous Struc-tures〔J〕. Journal of Geophysics and Engineering， 2007， 4（1）： 40-52.

〔10〕 YANG D H， WANG N， CHEN S， et al. An Explicit Algorithm Based on the Implicit Runge-Kutta Algorithm for Solving the Wave Equations〔J〕. Bulletin of the Seis-mological Society of America， 2009，99（6）： 3340-3354.

〔11〕 TONG P， YANG D H， HUA B L， et al. A High-Order Stereo-Modeling Method for Solving Wave Equations〔J〕. Bulletin of the Seismological Society of America， 2013， 103（2A）： 811-833.

〔12〕 QIU J X， LI T G， KHOO B C. Simulations of Compressible Two-Medium Flow by Runge-Kutta Discontinuous Galerkin Methods with the Ghost Fluid Method〔J〕. Communications in Computational Physics， 2008， 3（3）：479-504.

〔13〕 YANG D H， PENG J M， LU M， et al. Optimal Nearly-Analytic Discrete Approximation to the Scalar Wave Equation〔J〕. Bulletin of the Seismological Society of America ， 2006， 96（3）： 1114-1130.

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