Numerical modeling of biofilms

Graduation date: 2015We present a new mathematical model for the development of biofilm that extends\ud the nonlinear density-dependent continuum model introduced by Eberl et al. in 2001. It\ud is a coupled nonlinear density-dependent diffusion-reaction model for biomass spreading,\ud describing the interaction of nutrient availability and biomass production. The model by\ud Eberl has a degenerate and singular diffusion coefficient. The model considered in this\ud thesis relaxes the singularity but imposes an inequality constraint on the biomass amount.\ud We first consider a simplified zero-dimensional nonlinear ODE system. To understand\ud the basic behavior of the ODE system we use linearization and examine the phase plane.\ud We also consider several Finite Difference schemes to approximate the solutions including\ud Forward Euler, Sequential method and Newton's method.\ud Next we modify the PDE model by Eberl et al., by introducing a new density- dependent diffusion coefficient and introduce an inequality constraint. Applying Newton's\ud method, we discretize the system in space and time. The use of Neumann boundary\ud conditions allows us to study the morphology of biofilm as well as the dynamics of the total\ud amounts. Additionally, we impose a condition on the time step and run several numerical\ud experiments with varying initial conditions to show robustness of the new model