Efficient numerical solution of a simple discretization of Biot’s model
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[1] Universidad de Zaragoza
Universidad de Zaragoza
Zaragoza, España
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- Localización: Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 0370-3207, Nº. 80, 2025, págs. 7-46
- Idioma: inglés
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Resumen
This work presents a simple and efficient approach for the numerical solution of the single- phase flow problem in deformable porous media. To this end, Biot’s model is derived from basic principles of fluid and solid mechanics, and the numerical challenges associated with its discretization and the solution of the resulting algebraic systems are discussed. Piecewise linear finite element methods are considered as one of the simplest discretization strategies for this problem, and a suitable stabilization technique is introduced to ensure uniform stability properties and a monotone discrete scheme. To solve the algebraic systems arising from the stabilized discretization, efficient decoupled solvers are reviewed and theoretically analyzed. In particular, we propose an iterative coupling method and a non-iterative sequential method for solving the resulting stabilized scheme. The efficiency and robustness of both the discretization and the solution approaches are demonstrated.
