中国物理B ›› 2006, Vol. 15 ›› Issue (12): 2819-2827.doi: 10.1088/1009-1963/15/12/009

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A method of solving the stiffness problem in Biot's poroelastic equations using a staggered high-order finite-difference

赵海波1, 陈 浩1, 王秀明2   

  1. (1)Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080, China; (2)Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080, China;Australian Resources Research Centre, Australian Commonwealth Scientific and Industrial Research Organization,Bentley WA 6102, Australia
  • 收稿日期:2006-04-13 修回日期:2006-04-29 出版日期:2006-12-20 发布日期:2006-12-20
  • 基金资助:
    Project supported by the ``100 Talents Project" of the Chinese Academy of Sciences and the Major Program of the National Natural Science Foundation of China (Grant No 10534040).

A method of solving the stiffness problem in Biot's poroelastic equations using a staggered high-order finite-difference

Zhao Hai-Bo(赵海波)a)†, Wang Xiu-Ming(王秀明)a)b), and Chen Hao(陈浩)a)   

  1. a Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080, China; b Australian Resources Research Centre, Australian Commonwealth Scientific and Industrial Research Organization, Bentley WA 6102, Australia
  • Received:2006-04-13 Revised:2006-04-29 Online:2006-12-20 Published:2006-12-20
  • Supported by:
    Project supported by the ``100 Talents Project" of the Chinese Academy of Sciences and the Major Program of the National Natural Science Foundation of China (Grant No 10534040).

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摘要： In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Biot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.

关键词: porous media, stiffness, partition method, staggered grid, finite difference

Abstract: In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Biot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.

Key words: porous media, stiffness, partition method, staggered grid, finite difference

中图分类号:  (Elasticity, fracture, and flow)

  • 91.60.Ba
47.11.-j (Computational methods in fluid dynamics) 91.60.Np (Permeability and porosity) 91.60.Qr (Wave attenuation)