An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions
| Autor: | Mária Lukáčová-Medvi${ rm{ check{d}}}$ová, Șeyma Nur Özcan, Alina Chertock, Alexander Kurganov |
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| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Mean free path Decoupling (cosmology) Space (mathematics) Kinetic energy 01 natural sciences Quantitative Biology::Cell Behavior 010305 fluids & plasmas 010101 applied mathematics Modeling and Simulation 0103 physical sciences Convergence (routing) Path (graph theory) Applied mathematics Limit (mathematics) 0101 mathematics Scaling Mathematics |
| Zdroj: | Kinetic & Related Models. 12:195-216 |
| ISSN: | 1937-5077 |
| DOI: | 10.3934/krm.2019009 |
| Popis: | In this paper, we study two-dimensional multiscale chemotaxis models based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator which describes the velocity change of the cells. The parabolic scaling yields a non-dimensional kinetic model with a small parameter, which represents the mean free path of the cells. We propose a new asymptotic preserving numerical scheme that reflects the convergence of the studied micro-macro model to its macroscopic counterpart-the Patlak-Keller-Segel system-in the singular limit. The method is based on the operator splitting strategy and a suitable combination of the higher-order implicit and explicit time discretizations. In particular, we use the so-called even-odd decoupling and approximate the stiff terms arising in the singular limit implicitly. We prove that the resulting scheme satisfies the asymptotic preserving property. More precisely, it yields a consistent approximation of the Patlak-Keller-Segel system as the mean-free path tends to 0. The derived asymptotic preserving method is used to get better insight to the blowup behavior of two-dimensional kinetic chemotaxis model. |
| Databáze: | OpenAIRE |
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