Computational Aspects and Application of Numerical Simulations of Development of Biofilms Modelled with Systems of Stiff Evolutionary Partial Differential Equations




Zarva, Pavel

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University of Guelph


This paper considers biofilm growth models, a subclass of mesoscopic models, with multiple biological species and multiple chemical substrates, on which the growth of species is dependent, as well as with a molecular inter-species signal. The mathematical models are realized as systems of stiff quasi-linear diffusion-reaction partial differential equations (PDEs). These models are used to implement numerical simulations of biofilm development. Discretization of the PDE systems is done using the finite volume method with arithmetic flux averaging, and as a stiff time integrator with adaptive time steps. This results in a singular linear system corresponding to the associated system of ordinary differential equations. A Rosenbrock-Wanner (ROW) method is used to numerically solve such systems. This study is related to a research made by Dr. Hermann Eberl and Dr. Maryam Ghasemi, and it is focused on the extension, optimization and generalization, as well as on computational, runtime and numerical aspects of the simpler model studied in the respective research.



biofilm, partial differential equations, stiff differential equations, evolutionary differnetial equations, fortran, computational, parallel computing, BiCGStab, Rosenbrock-Wanner method, ROW method, scientific computing


Zarva P., Eberl H.J. (2020) Simulation Based Exploration of Bacterial Cross Talk Between Spatially Separated Colonies in a Multispecies Biofilm Community. In: Krzhizhanovskaya V. et al. (eds) Computational Science �?? ICCS 2020. ICCS 2020. Lecture Notes in Computer Science, vol 12143. Springer, Cham.