A central difference method with low numerical dispersion for solving the scalar wave equation

ABSTRACT In this paper, we propose a nearly‐analytic central difference method, which is an improved version of the central difference method. The new method is fourth‐order accurate with respect to both space and time but uses only three grid points in spatial directions. The stability criteria and...

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Published in:Geophysical Prospecting Vol. 60; no. 5; pp. 885 - 905
Main Authors: Yang, Dinghui, Tong, Ping, Deng, Xiaoying
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01-09-2012
Blackwell
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Summary:ABSTRACT In this paper, we propose a nearly‐analytic central difference method, which is an improved version of the central difference method. The new method is fourth‐order accurate with respect to both space and time but uses only three grid points in spatial directions. The stability criteria and numerical dispersion for the new scheme are analysed in detail. We also apply the nearly‐analytic central difference method to 1D and 2D cases to compute synthetic seismograms. For comparison, the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method are used to model acoustic wavefields. Numerical results indicate that the nearly‐analytic central difference method can be used to solve large‐scale problems because it effectively suppresses numerical dispersion caused by discretizing the scalar wave equation when too coarse grids are used. Meanwhile, numerical results show that the minimum sampling rate of the nearly‐analytic central difference method is about 2.5 points per minimal wavelength for eliminating numerical dispersion, resulting that the nearly‐analytic central difference method can save greatly both computational costs and storage space as contrasted to other high‐order finite‐difference methods such as the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method.
Bibliography:ark:/67375/WNG-MZMKH8ZZ-V
istex:EE8CB0A2AD5F2B2889EC88F4DBA1810ACAC6A74C
ArticleID:GPR1033
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0016-8025
1365-2478
DOI:10.1111/j.1365-2478.2011.01033.x