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Adaptive Moving Mesh Upwind Scheme for the Two-Species Chemotaxis Model

hal.structure.identifierDepartment of mathematics [North Carolina]
dc.contributor.authorCHERTOCK, Alina
hal.structure.identifierSouthern University of Science and Technology [SUSTech]
dc.contributor.authorKURGANOV, Alexander
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorRICCHIUTO, Mario
hal.structure.identifierDepartment of mathematics [North Carolina]
dc.contributor.authorWU, Tong
dc.date.accessioned2024-04-04T03:01:46Z
dc.date.available2024-04-04T03:01:46Z
dc.date.issued2019-03
dc.identifier.issn0898-1221
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192925
dc.description.abstractEnChemotaxis systems are used to model the propagation, aggregation and pattern formation of bacteria/cells in response to an external stimulus, usually a chemical one. A common property of all chemotaxis systems is their ability to model a concentration phenomenon-rapid growth of the cell density in small neighborhoods of concentration points/curves. More precisely, the solution may develop singular, spiky structures, or even blow up in finite time. Therefore, the development of accurate and computationally efficient numerical methods for the chemotaxis models is a challenging task. We study the two-species Patlak-Keller-Segel type chemotaxis system, in which the two species do not compete, but have different chemotactic sensitivities, which may lead to a significantly difference in cell density growth rates. This phenomenon was numerically investigated in [Kurganov and Lukáčová-Medvid'ová, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), pp. 131-152] and [Chertock et al., Adv. Comput. Math., 44 (2018), pp. 327-350], where second-and higher-order methods on uniform Cartesian grids were developed. However, in order to achieve high resolution of the density spikes developed by the species with a lower chemotactic sensitivity, a very fine mesh had to be utilized and thus the efficiency of the numerical method was affected. In this work, we consider an alternative approach relying on mesh adaptation, which helps to improve the approximation of the singular structures evolved by chemotaxis models. We develop, in particular, an adaptive moving mesh (AMM) finite-volume semi-discrete upwind method for the two-species chemotaxis system. The proposed AMM technique allows one to increase the density of mesh nodes at the blowup regions. This helps to substantially improve the resolution while using a relatively small number of finite-volume cells.
dc.language.isoen
dc.publisherElsevier
dc.subject.enTwo-species chemotaxis system
dc.subject.enAdaptive moving mesh (AMM) method
dc.subject.enFinite- volume upwind method
dc.subject.enSingular (spiky) solutions
dc.title.enAdaptive Moving Mesh Upwind Scheme for the Two-Species Chemotaxis Model
dc.typeArticle de revue
dc.identifier.doi10.1016/j.camwa.2019.01.021
dc.subject.halInformatique [cs]/Modélisation et simulation
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalComputers & Mathematics with Applications
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02064581
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02064581v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Computers%20&%20Mathematics%20with%20Applications&rft.date=2019-03&rft.eissn=0898-1221&rft.issn=0898-1221&rft.au=CHERTOCK,%20Alina&KURGANOV,%20Alexander&RICCHIUTO,%20Mario&WU,%20Tong&rft.genre=article


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