Numerical methods for a one-dimensional non-linear Biot’s model

Staggered finite difference methods for a one-dimensional Biot’s problem are considered. The permeability tensor of the porous medium is assumed to depend on the strain, thus yielding a non-linear model. Some strong two-side estimates for displacements and for pressure are provided and convergence r...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-02, Vol.293, p.62-72
Main Authors: Gaspar, Francisco J., Lisbona, Francisco J., Matus, Piotr, Tuyen, Vo Thi Kim
Format: Article
Language:English
Subjects:
Convergence
Finite difference method
Finite-difference scheme
Mathematical analysis
Mathematical models
Maximum principle
Non-linear Biot’s model
Nonlinearity
Porous media
Strain
Tensors
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Summary:Staggered finite difference methods for a one-dimensional Biot’s problem are considered. The permeability tensor of the porous medium is assumed to depend on the strain, thus yielding a non-linear model. Some strong two-side estimates for displacements and for pressure are provided and convergence results in the discrete L2-norm are proved. Numerical examples are given to illustrate the good performance of the proposed numerical approach.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.03.039