趋化现象动力学模型的渐近保持格式

IF 0.3 Q4 MATHEMATICS Communications in Applied and Industrial Mathematics Pub Date : 2015-07-18 DOI:10.2478/caim-2018-0010

A. Bellouquid, Jacques Tagoudjeu

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引用次数: 7

摘要

摘要本文提出了一种求解趋化现象动力学模型的数值方法。该方案在小参数下均匀稳定，符合流体扩散极限(Keller-Segel模型)。我们的方法是基于微观-宏观分解，这导致动力学模型的等效公式，耦合动力学方程与宏观方程。该方法通过各种测试用例进行验证，并与其他标准方法进行比较。

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An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

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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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.