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Numerical methods for a nonlinear reaction-diffusion system modelling a batch culture of biofilm

AuthorsBalsa-Canto, Eva ; López-Núñez, Alejandro; Vázquez, Carlos
Continuum models
Nonlinear reaction–diffusion equations
Numerical methods
Issue Date2017
CitationApplied Mathematical Modelling 41: 164-179 (2017)
AbstractA biofilm is usually defined as a layer of bacterial cells anchored to a surface. These cells are embedded into a polymer matrix that keeps them attached to each other and to a solid surface. Among a large variety of biofilms, in this paper we consider batch cultures. The mathematical model is formulated in terms of a quasilinear system of diffusion–reaction equations for biomass and nutrients concentrations, which exhibits possible degeneracy and singularities in the nonlinear diffusion coefficient. In the present paper, we propose a set of efficient numerical methods that speeds up the solution of the model. Mainly, Crank–Nicolson finite differences techniques for discretisation are combined with a Newton algorithm for the nonlinearities. Moreover, some numerical examples show the expected behaviour of the biomass and nutrients concentrations and also clearly illustrate some theoretically proved qualitative properties related to exponential decays or convergence to a critical biomass concentration depending on the values of the model parameters
Description16 páginas, 15 figuras, 3 tablas
Publisher version (URL)http://dx.doi.org/10.1016/j.apm.2016.08.020
Appears in Collections:(IIM) Artículos
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