Speaker
Description
Biofilms describe a the colonization of bacteria on surfaces. They attract more and more bacteria and express a extracellular matrix (EPS). By that, a growing solid domain is formed. Biofilms mainly form in fluid domains. The bacteria are described as concentrations in our continuum description, where attraction and growth is described by an advection-diffusion-reaction equation (PDE) and the growth of EPS by a source term in the mass-balance equation. We solve the coupled fluid and growing solid (FSI) system using an interface tracking method: the arbitrary Lagrangian-Eulerian (ALE) approach for finite elements. Thus, the solid domain is modeled in Lagrangian coordinates and the fluid domain is modeled in Eulerian coordinates. In order to ensure that we are able to resolve narrow areas resulting from the growth process accurate, we solve a biharmonic extension with a mixed formulation as an additional partial differential equation. The resulting model is a highly nonlinear, nonstationary, coupled chemical-growth-FSI variational-monolithic system in which we seek four solution variables: velocities, pressure, displacements, concentrations. As the biofilm growth is a slow process (days), a implicit backward Euler scheme is used as time-stepping scheme. Then, a Galerkin finite element scheme is employed for spatial discretization with inf-sup stable finite elements for the flow part. A Newton method is used for linearization. Therein, the arising linear systems are solved with a sparse direct solver. Our approach is substantiated with several numerical tests on different mesh levels and time step sizes in order to investigate computational stability.
