A fluid dynamics model of the growth of phototrophic biofilms.

Fabrizio Clarelli; Cristiana Di Russo; Roberto Natalini; Magali Ribot

doi:10.1007/s00285-012-0538-5

A fluid dynamics model of the growth of phototrophic biofilms.

Fabrizio Clarelli ¹ Cristiana Di Russo ² Roberto Natalini ¹ Magali Ribot ^{3, 4}

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"

2 ICJ - Institut Camille Jordan

3 JAD - Laboratoire Jean Alexandre Dieudonné

4 INRIA Sophia Antipolis - COFFEE

Abstract : A system of nonlinear hyperbolic partial differential equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simulations will be presented in one and more space dimensions in the particular case of cyanobacteria biofilms. Besides, the numerical scheme we present is able to deal in a natural and effective way with regions where one of the phases is vanishing.

Keywords : Fluid dynamics model Hyperbolic equations Phototrophic biofilms Front propagation

Document type :

Journal articles

Journal of Mathematical Biology, Springer Verlag (Germany), 2013, 66 (7), pp.1387-1408. <10.1007/s00285-012-0538-5>

Domain :

Mathematics / Numerical Analysis

Mathematics / Analysis of PDEs

https://hal.archives-ouvertes.fr/hal-00764378
Contributor : Magali Ribot <>
Submitted on : Wednesday, December 12, 2012 - 10:03:10 PM
Last modification on : Tuesday, November 5, 2013 - 5:26:39 PM

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A fluid dynamics model of the growth of phototrophic biofilms.

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