An asymptotic preserving scheme for kinetic models for chemotaxis phenomena

TL;DR

This paper introduces an asymptotic preserving numerical scheme for kinetic models of chemotaxis, ensuring stability across regimes and effectively coupling microscopic and macroscopic dynamics.

Contribution

The paper presents a novel micro-macro decomposition-based scheme that maintains stability and consistency with the fluid-diffusion limit for chemotaxis kinetic models.

Findings

Scheme is uniformly stable with respect to small parameters

Validated with various test cases

Compared favorably to standard methods

Abstract

In this paper, we propose a numerical scheme to solve the kinetic model for chemotaxis phenomena. Formally, this scheme is shown to be uniformly stable with respect to the small parameter, consistent with the fluid-diffusion 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 with various test cases and compared to other standard methods.