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Kinetic-fluid derivation and mathematical analysis of nonlocal cross-diffusion-fluid system

Abstract : In this paper, we propose a nonlocal cross-diffusion-fluid system describing the dynamic of interacting multi-populations living in a Newtonian fluid. First, we derive our nonlocal cross-diffusion-fluid system from a nonlocal kinetic-fluid model by performing the micro-macro decomposition method. Second, we prove the existence of weak solutions for the proposed system by applying the nonlinear Galerkin method within a priori estimates and compactness arguments. Based on micro-macro decomposition, we propose and we develop an asymptotic preserving numerical scheme. Finally, we deal with the computational results of the proposed system.
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https://hal.inria.fr/hal-02142040
Contributor : Mostafa Bendahmane <>
Submitted on : Tuesday, May 28, 2019 - 1:14:47 PM
Last modification on : Thursday, March 5, 2020 - 3:32:51 PM

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Mostafa Bendahmane, Fahd Karami, Mohammed Zagour, Driss Meskine. Kinetic-fluid derivation and mathematical analysis of nonlocal cross-diffusion-fluid system. Applied Mathematical Modelling, Elsevier, In press, ⟨10.1016/j.apm.2019.11.036⟩. ⟨hal-02142040⟩

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