Numerical solutions of a 2D fluid problem coupled to a nonlinear non-local reaction-advection-diffusion problem for cell crawling migration in a discoidal domain

Solutions numérique pour un problème fluide 2D dans un domaine disque couplé à un problème non linéaire et non local de réaction-advection-diffusion pour la migration cellulaire

Christèle Etchegaray (1) , Nicolas Meunier (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and a reaction-advection-diffusion problem. Moreover, the advection velocity depends on boundary values, making the problem nonlinear and non local. \par For a discoidal domain, numerical solutions can be obtained using the finite volume method on the polar formulation of the model. Simulations show that different migration behaviours can be captured.

Mots clés: finite volume method; Darcy fluid; nonlinear non-local reaction-advection-diffusion problem; finite volume method; nonlinear non-local reaction-advection-diffusion problem; 2D cell migration; Darcy fluid

Domaines: Analyse numérique [math.NA]

Christèle Etchegaray, Nicolas Meunier. Numerical solutions of a 2D fluid problem coupled to a nonlinear non-local reaction-advection-diffusion problem for cell crawling migration in a discoidal domain. 2017. ⟨hal-01760518⟩