Kinetic-fluid derivation and mathematical analysis of nonlocal cross-diffusion-fluid system
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
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Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Language
en
Article de revue
This item was published in
Applied Mathematical Modelling. 2019
Elsevier
Date
2019English 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 ...Read more >
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.Read less <
English Keywords
Nonlocal diffusion
Kinetic-fluid theory
Nonlinear cross-diffusion
Nonlinear Galerkin method
Asymptotic preserving scheme
Pattern-formation
Finite volume method
Finite element method
Origin
Hal imported