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Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem

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Abstract

We consider the solution of a two-phase miscible displacement problem on dynamic adaptive meshes using the mimetic finite difference method. The mimetic finite difference method is employed to discretize the Darcy law and the mass fraction advection-dispersion equation. We propose modifications to the mimetic finite difference method: to reproduce two-point flux approximation on \(\mathbb{K}\)-orthogonal grids and address degenerate advection-diffusion problems. We validate the method and demonstrate its applicability to the viscous fingering problem with adaptive mesh refinement.

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Funding

This work has been supported by the Ministry of Education and Science of the Russian Federation, agreement no. 075-15-2022-286.

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Authors and Affiliations

  1. Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University, Qatar Foundation, Doha, Qatar

    A. Abushaikha

  2. Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences, 119991, Moscow, Russia

    K. Terekhov

  3. Sirius University of Science and Technology, 354340, Sochi, Russia

    K. Terekhov

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  1. A. Abushaikha
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Abushaikha, A., Terekhov, K. Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem. Lobachevskii J Math 45, 143–154 (2024). https://doi.org/10.1134/S1995080224010025

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