A spatially stabilized TDG based finite element framework for modeling biofilm growth with a multi-dimensional multi-species continuum biofilm model

We consider a model for biofilm growth in the continuum mechanics framework, where the growth of different components of biomass is governed by a time dependent advection-reaction equation. The recently developed time-discontinuous Galerkin (TDG) method combined with two different stabilization techniques, namely the Streamline Upwind Petrov Galerkin (SUPG) method and the finite increment calculus (FIC) method, are discussed as solution strategies for a multi-dimensional multi-species biofilm growth model. The biofilm interface in the model is described by a convective movement following a potential flow coupled to the reaction inside of the biofilm. Growth limiting substrates diffuse through a boundary layer on top of the biofilm interface. A rolling ball method is applied to obtain a boundary layer of constant height. We compare different measures of the numerical dissipation and dispersion of the simulation results in particular for those with non-trivial patterns. By using these measures, a comparative study of the TDG-SUPG and TDG-FIC schemes as well as sensitivity studies on the time step size, the spatial element size and temporal accuracy are presented.