We consider a nonlinear coupled system of parabolic variational (in)equalities modeling biofilm– nutrient dynamic in porous media coupled to Brinkman flow model. Microbial growth in porous media is affected by nutrient supply and ambient fluid flow. It is also constrained by available space. We approximate the system using a mixed finite element method of the lowest order of the Raviart-Thomas element due to the low regularity of solutions of parabolic variational inequalities. We show the well-posedness of the discrete model and derive an optimal error estimate of the first order, which is validated experimentally. Moreover, we conduct 2D simulations to investigate the behavior of biofilm growth in simple and complex pore-scale geometries.

This is joint work with Prof. Malgorzata Peszynska from Oregon State University and Dr. Choah Shin from Ab Initio Software.