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Adaptive mesh refinement for flow and transport problem in heterogeneous porous media

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  • Amor, Hanen
  • Benkhaldoun, Fayssal

Abstract

This paper presents an adaptive mesh refinement strategy for modeling the flow and transport of contaminants in porous media. These phenomena are modeled by a system of equations that combine Darcy’s law and the diffusion-convection equation. A combined finite volume and finite element discretization is used to discretize the coupled system. A guaranteed a posteriori error estimator, derived from an H(div)-conforming flux reconstruction, is computed and followed by an appropriate method of local refinement and coarsening of mesh elements in two and three dimension to minimize the difference between a discretized solution and a continuous solution in the context of industrial applications. The method is implemented within the MELODIE software developed by the ASNR in order to assess the safety of a deep geological disposal for radioactive waste, and is illustrated through a realistic application of flow and transport in heterogeneous porous media.

Suggested Citation

  • Amor, Hanen & Benkhaldoun, Fayssal, 2026. "Adaptive mesh refinement for flow and transport problem in heterogeneous porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 766-789.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:766-789
    DOI: 10.1016/j.matcom.2025.06.020
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