A new time–space domain high-order finite-difference method for the acoustic wave equation

Handle URI:
http://hdl.handle.net/10754/597347
Title:
A new time–space domain high-order finite-difference method for the acoustic wave equation
Authors:
Liu, Yang; Sen, Mrinal K.
Abstract:
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
Citation:
Liu Y, Sen MK (2009) A new time–space domain high-order finite-difference method for the acoustic wave equation. Journal of Computational Physics 228: 8779–8806. Available: http://dx.doi.org/10.1016/j.jcp.2009.08.027.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Dec-2009
DOI:
10.1016/j.jcp.2009.08.027
Type:
Article
ISSN:
0021-9991
Sponsors:
We thank the editor Dr. Alvin Bayliss and three anonymous reviewers for constructive criticism of our paper. Liu would like to thank China Scholarship Council for their financial support for this research and UTIG for providing with the facilities. This research is also partially supported by NSFC under Contract No. 40839901, the National “863” Program of China under Contract No. 2007AA06Z218 and KAUST AEA grant at UT Austin.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Yangen
dc.contributor.authorSen, Mrinal K.en
dc.date.accessioned2016-02-25T12:31:14Zen
dc.date.available2016-02-25T12:31:14Zen
dc.date.issued2009-12en
dc.identifier.citationLiu Y, Sen MK (2009) A new time–space domain high-order finite-difference method for the acoustic wave equation. Journal of Computational Physics 228: 8779–8806. Available: http://dx.doi.org/10.1016/j.jcp.2009.08.027.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2009.08.027en
dc.identifier.urihttp://hdl.handle.net/10754/597347en
dc.description.abstractA new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.en
dc.description.sponsorshipWe thank the editor Dr. Alvin Bayliss and three anonymous reviewers for constructive criticism of our paper. Liu would like to thank China Scholarship Council for their financial support for this research and UTIG for providing with the facilities. This research is also partially supported by NSFC under Contract No. 40839901, the National “863” Program of China under Contract No. 2007AA06Z218 and KAUST AEA grant at UT Austin.en
dc.publisherElsevier BVen
dc.subjectAcoustic wave equationen
dc.subjectArbitrary-order accuracyen
dc.subjectDispersion analysisen
dc.subjectDispersion relationen
dc.subjectFinite-differenceen
dc.subjectNumerical modelingen
dc.subjectOptimal finite-difference stencil lengthen
dc.subjectPlane wave theoryen
dc.subjectSecond-order spatial derivativesen
dc.subjectStability conditionen
dc.subjectStaggered-grid finite-differenceen
dc.subjectTime-space domainen
dc.titleA new time–space domain high-order finite-difference method for the acoustic wave equationen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionChina University of Petroleum - Beijing, Beijing, Chinaen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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