High-order compact difference schemes based on the local one-dimensional method for high-dimensional nonlinear wave equations

被引：0
作者：
Mengling Wu
Zhi Wang
Yongbin Ge
机构：
[1] Dalian Minzu University,School of Science
[2] Ningxia University,Institute of Applied Mathematics and Mechanics
来源：
Computational Geosciences | 2023年 / 27卷
关键词：
High-dimensional nonlinear wave equation; Variable coefficient; Local one-dimensional; Fourth-order compact scheme;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, two compact difference schemes are established for solving two-dimensional (2D) and three-dimensional (3D) nonlinear wave equations with variable coefficients, respectively, by using the local one-dimensional (LOD) method and the fourth-order compact difference approximation formulas of the second-order derivatives. Firstly, a four-step fourth-order compact scheme is derived to solve the 2D nonlinear wave equation. The stability of the scheme 2for solving the linear equation is analyzed by the discrete Fourier method, which shows that it is conditionally stable. Then, the method is extend to solve the 3D nonlinear wave equation and stability condition for the linear equation is also analyzed. Finally, numerical experiments are conducted to verify the accuracy and stability of the proposed schemes.
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页码：687 / 705
页数：18
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[1]  
Li L(2021)FD wave 3D: a MATLAB solver for the 3D anisotropic wave equation using the finite-difference method Comput. Geosci. 25 1565-1578
[2]  
Tan J(2018)A new central compact finite difference scheme with high spectral resolution for acoustic wave equation J. Comput. Phys. 366 191-206
[3]  
Zhang D(2015)Comparison of finite difference schemes for the wave equation based on dispersion J. Appl. Math. Phys. 3 1544-1562
[4]  
Wang Z(2018)Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media Appl. Math. Comput. 321 385-400
[5]  
Li J(2014)On the dispersion, stability and accuracy of a compact higher-order finite difference scheme for 3D acoustic wave equation J. Comput. Appl. Math. 270 571-583
[6]  
Wang B(2007)Finite difference time domain dispersion reduction schemes J. Comput. Phys. 221 422-438
[7]  
Xu Y(2010)A split-step algorithm with effectively suppressing the numerical dispersion for 3D seismic propagation modeling Bull. Seismol. Soc. Am. 100 1470-1484
[8]  
Chen X(2012)A central difference method with low numerical dispersion for solving the scalar wave equation Geophys. Prospect. 60 885-905
[9]  
Abdulkadir Y(2009)A new time space domain high-order finite-difference method for the acoustic wave equation J. Comput. Phys. 228 8779-8806
[10]  
Liao W(2016)A new mimetic scheme for the acoustic wave equation J. Comput. Appl. Math. 295 2-12
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