Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part I: Numerical Scheme and Convergence Results
Jason F. Hammond, Elizabeth J. Stewart, John G. Younger, Michael J. Solomon, David M. Bortz

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 98, No. 3, pp. 295-340, 2014
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Keywords Navier-Stokes equation, biofilm, immersed boundary method, computational fluid dynamics, multigrid, viscoelastic fluid.

The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion of erosion and detachment into the simulation. We use the incompressible Navier-Stokes (N-S) equations to describe the motion of the flowing fluid and discretize the fluid equations using finite differences. We use a geometric multigrid method to solve the resulting equations at each time step. We note that the use of multigrid is necessary because of the dramatically different densities and viscosities between the biofilm and the surrounding fluid. We investigate and simulate the model in both two and three dimensions. We also note that our method differs from several previous attempts of using IBM for modeling biofilm/flow interactions in the following ways: the density and viscosity of the biofilm can differ substantially from the surrounding fluid, and the Lagrangian node locations correspond to experimentally measured bacterial cell locations from 3D images taken of Staphylococcus epidermidis in a biofilm. In the followup article, we will present the results of the validation of this model and calibration to several experimental scenarios.

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