A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis
Chemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms,...
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EDP Sciences
2018-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201861068 |
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doaj-fe6a0038f1474239be0a6ccea2b45e7c2021-07-15T14:14:22ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592018-01-0161689210.1051/proc/201861068proc_esaim2018_068A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxisRibot MagaliChemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms, a semi-linear system based on the hyperbolic heat equation (or dissipative waves equation) and a quasi-linear system based on incompressible Euler equation. These models possess relatively stiff solutions and well-balanced and asymptotic-preserving schemes are necessary to approximate them accurately. The aim of this article is to present various techniques of well-balanced and asymptotic-preserving schemes for the two hyperbolic models for chemotaxis.https://doi.org/10.1051/proc/201861068 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ribot Magali |
| spellingShingle |
Ribot Magali A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ESAIM: Proceedings and Surveys |
| author_facet |
Ribot Magali |
| author_sort |
Ribot Magali |
| title |
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| title_short |
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| title_full |
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| title_fullStr |
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| title_full_unstemmed |
A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| title_sort |
survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis |
| publisher |
EDP Sciences |
| series |
ESAIM: Proceedings and Surveys |
| issn |
2267-3059 |
| publishDate |
2018-01-01 |
| description |
Chemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms, a semi-linear system based on the hyperbolic heat equation (or dissipative waves equation) and a quasi-linear system based on incompressible Euler equation. These models possess relatively stiff solutions and well-balanced and asymptotic-preserving schemes are necessary to approximate them accurately. The aim of this article is to present various techniques of well-balanced and asymptotic-preserving schemes for the two hyperbolic models for chemotaxis. |
| url |
https://doi.org/10.1051/proc/201861068 |
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AT ribotmagali asurveyonwellbalancedandasymptoticpreservingschemesforhyperbolicmodelsforchemotaxis AT ribotmagali surveyonwellbalancedandasymptoticpreservingschemesforhyperbolicmodelsforchemotaxis |
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