Finite volume method for one dimensional biot poroelasticity system in multilayered domains

Document Type : Research Article

Authors

Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Abstract

R. Ewing, O. Liev, R. Lazarov and A. Naumovich in [1] proposed a finite volume discretization for one dimensional Biot poroelasticity system in multilayer domains. Their discretization and exact solution are invalid. We derive valid discretization and exact solution. Finally, our numerical solution is compared with known exact solution in discrete L2 norm.

Keywords

References

1. Ewing, R., Liev, O., Lazarov, R. and A. Naumovich, On convergence of certain finite volume difference discretizations for 1D poroelasticity interface problems, Wiley Inter Science, DOI 10. 1002/ num. 20184, (2006).
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4. Korsawe, J. and Starke, G., A least - squares mixed finite element method for Biot’s consolidation problem in porous media , SIAM Journal on numerical analysis, 43 (1), (2005), 318 - 339.
5. Liev, O., Finite volume discretizations for elliptic problems with discontinuous coefficients, Habilitation, University of Kaiserslautern, (2002).
6. Naumovich, A., Efficient numerical methods for the Biot poroelasticity system in multilayered domains, Vom fachbereich mathematik, Der universitat kaiserslautern, Zur verleihung des akademischen grades, (2007).
7. Versteeg, H. K. and Malalaskera, W., An introduction to computational fluid dynamics: The finite volume method, Longman scientific and technical, (1995).
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