Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

An asymptotic preserving and well-balanced scheme for a chemotaxis model

christophe berthon

universite de nantes


This presentation concerns the numerical approximation of a PDE system which models cell movements according to a chemoattractant concentration. The system under consideration turns out to couple a hyperbolic system with a diffusive equation. The solutions of such a model satisfy several properties to be preserved at the numerical level. Indeed, the solutions may contain vacuum, satisfy steady regimes and asymptotic regimes. By deriving a judicious approximate Riemann solver, a finite volume method is designed in order to exactly preserve the steady regimes of particular physical interest. Moreover, the scheme is able to deal with vacuum regions and it preserves the asymptotic regimes.