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Journal Articles Applied Mathematical Modelling Year : 2019

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

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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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Dates and versions

hal-02142040 , version 1 (28-05-2019)

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Cite

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