Level sets and extended finite elements for evolution of microbial biofilms and of precipitates in elastic media

A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method, for simulating evolution of bacterial biofilms and of elastic precipitates in two-dimensions is presented. The coupling of the XFEM with a comprehensive level set update scheme with velocity extensions makes updating the interface fast and accurate without needing remeshing. The combined numerical method is computationally attractive to solve free boundary problems with moving boundaries, discontinuities, or singularities.;The combined numerical method is used to treat the growth of biofilms in two dimensions. The model considers: (1) fluid flow around the biofilm surface, (2) the advection-diffusion and reaction of substrate, (3) variable biomass volume fraction, and 4) erosion due to the interfacial shear stress at the biofilm-fluid interface. The 1D results we get are in excellent agreement with previous 1D results obtained using finite difference methods. Our 2D biofilm growth results are in good agreement with those presented in [1]. Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated evolution results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached.;The combined method is used to simulate the diffusional evolution of microstructures in binary alloys in two dimensions in the absence of elastic fields and also in the presence of elastic fields. The model considers: (1) the elastic stress due to the misfit between the particle and matrix, (2) diffusion of component 2 of the binary mixture matrix, (3) elastic stress modified Gibbs-Thompson equation for interfacial compositions, and (4) the particle evolution given by the mass balance equation. The formulation is general enough to consider the anisotropy and inhomogeneity of the elastic properties of the precipitate and matrix. The precipitate-matrix interfaces are tracked using the level set method. Growing shapes are dendritic while equilibrium shapes are squarish and in this respect our simulation results are in good agreement with those presented in [2, 3].