<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena"}

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...

An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

Published Online: Dec 19, 2018

Page range: 61 - 75

Received: Sep 30, 2016

Accepted: Jan 23, 2018

DOI: https://doi.org/10.2478/caim-2018-0010

Keywords
Asymptotic preserving scheme, Kinetic theory, Micro-macro decomposition, Chemotaxis phenomena

© 2018 Abdelghani Bellouquid, Jacques Tagoudjeu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

Published Online: Dec 19, 2018

Page range: 61 - 75

Received: Sep 30, 2016

Accepted: Jan 23, 2018

DOI: https://doi.org/10.2478/caim-2018-0010

KeywordsAsymptotic preserving scheme, Kinetic theory, Micro-macro decomposition, Chemotaxis phenomena

© 2018 Abdelghani Bellouquid, Jacques Tagoudjeu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Asymptotic preserving scheme, Kinetic theory, Micro-macro decomposition, Chemotaxis phenomena