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Volume 28, Issue 2
Stability Analysis for Wave Simulation in 3D Poroelastic Media with the Staggered-Grid Method

Wensheng Zhang

Commun. Comput. Phys., 28 (2020), pp. 743-767.

Published online: 2020-06

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  • Abstract

In this paper, a new approach is proposed to analyse the stability of high-order staggered-grid finite difference schemes for the three-dimensional (3D) poroelastic wave propagation. The standard staggered-grid schemes with different order accuracy in space are constructed based on the first-order hyperbolic velocity-stress system of the governing equations (i.e., Biot's equations). The new analysis method is based on von Neumann analysis. The obtained 3D stability is an explicit restriction for time step, which only depends on the coefficients of the difference operators and the material parameters of poroelastic media and so it can be computed easily. Moreover, the analysis has good generality and can be applied directly to the staggered-grid schemes for 3D elastic wave. Numerical computations with the perfectly matched layer in split formation are implemented to illustrate the effectiveness of the schemes for 3D poroelastic wave propagation. The method in this paper can be expected to analyse the stability for other staggered-grid schemes.

  • Keywords

3D, stability analysis, poroelastic media, wave propagation, staggered-grid.

  • AMS Subject Headings

35L05, 65C20, 65N12, 65N06, 74S20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-743, author = {Zhang , Wensheng}, title = {Stability Analysis for Wave Simulation in 3D Poroelastic Media with the Staggered-Grid Method}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {2}, pages = {743--767}, abstract = {

In this paper, a new approach is proposed to analyse the stability of high-order staggered-grid finite difference schemes for the three-dimensional (3D) poroelastic wave propagation. The standard staggered-grid schemes with different order accuracy in space are constructed based on the first-order hyperbolic velocity-stress system of the governing equations (i.e., Biot's equations). The new analysis method is based on von Neumann analysis. The obtained 3D stability is an explicit restriction for time step, which only depends on the coefficients of the difference operators and the material parameters of poroelastic media and so it can be computed easily. Moreover, the analysis has good generality and can be applied directly to the staggered-grid schemes for 3D elastic wave. Numerical computations with the perfectly matched layer in split formation are implemented to illustrate the effectiveness of the schemes for 3D poroelastic wave propagation. The method in this paper can be expected to analyse the stability for other staggered-grid schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0234}, url = {http://global-sci.org/intro/article_detail/cicp/16952.html} }
TY - JOUR T1 - Stability Analysis for Wave Simulation in 3D Poroelastic Media with the Staggered-Grid Method AU - Zhang , Wensheng JO - Communications in Computational Physics VL - 2 SP - 743 EP - 767 PY - 2020 DA - 2020/06 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2017-0234 UR - https://global-sci.org/intro/article_detail/cicp/16952.html KW - 3D, stability analysis, poroelastic media, wave propagation, staggered-grid. AB -

In this paper, a new approach is proposed to analyse the stability of high-order staggered-grid finite difference schemes for the three-dimensional (3D) poroelastic wave propagation. The standard staggered-grid schemes with different order accuracy in space are constructed based on the first-order hyperbolic velocity-stress system of the governing equations (i.e., Biot's equations). The new analysis method is based on von Neumann analysis. The obtained 3D stability is an explicit restriction for time step, which only depends on the coefficients of the difference operators and the material parameters of poroelastic media and so it can be computed easily. Moreover, the analysis has good generality and can be applied directly to the staggered-grid schemes for 3D elastic wave. Numerical computations with the perfectly matched layer in split formation are implemented to illustrate the effectiveness of the schemes for 3D poroelastic wave propagation. The method in this paper can be expected to analyse the stability for other staggered-grid schemes.

Wensheng Zhang. (2020). Stability Analysis for Wave Simulation in 3D Poroelastic Media with the Staggered-Grid Method. Communications in Computational Physics. 28 (2). 743-767. doi:10.4208/cicp.OA-2017-0234
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