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Simulation of a filtration in a deformable porous medium. A numerical approach. (English) Zbl 0902.76091

We present some numerical computations completed by convergence and stability results for a nonstandard problem of filtration through a porous medium with a free boundary. In the medium, a small number of solid micro-particles can be removed and transported by the flow through the medium itself. We discuss the existence and uniqueness of a classical solution, and transform the original free-boundary problem in a system of state-dependent delay equations. Finally, we establish the existence and uniqueness of a “classical” solution for the new model, and prove convergence and stability.

MSC:

76S05 Flows in porous media; filtration; seepage
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
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References:

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[2] BERTACCINI D., New numerical results for a filtration in a porous medium with a free boundary, to appear.; BERTACCINI D., New numerical results for a filtration in a porous medium with a free boundary, to appear. · Zbl 0902.76091
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