An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

Bellouquid, Abdelghani; Tagoudjeu, Jacques

doi:10.2478/caim-2018-0010

Abstract

In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

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An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

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