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 [Villeurbanne]
3 JAD - Laboratoire Jean Alexandre Dieudonné
4 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
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
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Journal of Mathematical Biology, Springer Verlag (Germany), 2013, 66 (7), pp.1387-1408. 〈10.1007/s00285-012-0538-5〉
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Fabrizio Clarelli, Cristiana Di Russo, Roberto Natalini, Magali Ribot. A fluid dynamics model of the growth of phototrophic biofilms.. Journal of Mathematical Biology, Springer Verlag (Germany), 2013, 66 (7), pp.1387-1408. 〈10.1007/s00285-012-0538-5〉. 〈hal-00764378〉

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