Parallel Simulations of Biofilm Flow Using the Modified Cahn-Hilliard Equation

Abstract

We present a 2D parallel implementation of the modified Cahn-Hilliard equation for the simulation of a biofilm in an aqueous enviroment. Biofilms are attached microbial communities made of many different components and can have both positive and negative effects. They can be used for bioremediation but also are the cause of the majority of chronic infections. It is for these reasons that we study them. Due to their composition being mostly water we choose to model them as an incompressible fluid. We used a visco-elastic phase separation model based on the modified Cahn-Hilliard equation and the Flory-Huggins energy density. We present results of a simulation showing detachment of a biofilm protrusion from a base layer of biofilm due to the flow over the biofilm. The parallelization was accomplished using PETSc (Portable, Extensible Toolkit for Scientific Computing), specifically the DMDA abstraction layer within PETSc. DMDA provides a useful interface for the solution of linear systems arising from structured grid discretizations. We evaluate the parallel performance of the implementation with a strong scaling test and calculate the speedup for various mesh sizes.