Vivette Girault, María González Taboada, Frédéric Hecht, Kumbakonam R. Rajagopal, A model for flow in deformable porous media, Vol. 2023 (2023), Article ID 20, pp. 1-44

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DOI: 10.23952/cot.2023.20

Received September 20, 2022; Accepted January 19, 2023; Published April 17, 2023


Abstract. Within the context of mixture theory, we consider a linearized model for the flow of a fluid though a deformable porous elastic solid, where with respect to the fluid, the solid is undergoing small but not negligible velocity. Albeit linear, the corresponding system of equations is fairly complex, because it is coupled by the solid and fluid velocities. The theoretical analysis (existence and uniqueness of solutions) of the system as well as the numerical analysis (uniform stability of the discrete solution) of its discretized version are done by superposition: splitting the solid’s displacement into a part that depends only on the data and a part that depends on the velocity of the fluid. A simple time lagging decoupling algorithm is studied and a sharper iterative algorithm proposed at the end. Numerical experiments confirm the performance of the numerical scheme and the validity of the model.


How to Cite this Article:
V. Girault, M. González Taboada, F. Hecht, K.R. Rajagopal, A model for flow in deformable porous media, Commun. Optim. Theory 2023 (2023) 20.