A combined extended finite element and level set method for biofilm growth

By Ravindra Duddu, Stéphane P.A. Bordas, David L. Chopp, Brian Moran. 2008

149 citations recorded by the source corpus.

This paper presents a computational technique based on the extended finite element method (XFEM) and the level set method for the growth of biofilms. The discontinuous‐derivative enrichment of the standard finite element approximation eliminates the need for the finite element mesh to coincide with the biofilm–fluid interface and also permits the introduction of the discontinuity in the normal derivative of the substrate concentration field at the biofilm–fluid interface. The XFEM is coupled with a comprehensive level set update scheme with velocity extensions, which makes updating the biofilm interface fast and accurate without need for remeshing. The kinetics of biofilms are briefly given and the non‐linear strong and weak forms are presented. The non‐linear system of equations is solved using a Newton–Raphson scheme. Example problems including 1D and 2D biofilm growth are presented to illustrate the accuracy and utility of the method. The 1D results we obtain are in excellent agreement with previous 1D results obtained using finite difference methods. Our 2D results that simulate finger formation and finger‐tip splitting in biofilms illustrate the robustness of the present computational technique. Copyright © 2007 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Mechanics of Materials, Surfaces, Coatings and Films

View Paper: https://www.semanticscholar.org/paper/4a358835fd3d9d849b371b3f1366acb3843a72de

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In Computational Mechanics

In Mechanics of Materials

In Surfaces, Coatings and Films

Stéphane P.A. Bordas

Citations in the corpus

Strain smoothing in FEM and XFEM (2010, methodology): “XFEM was used successfully for crack propagation and other fields in computational physics [23,25,24,26,33].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, background): “To handle discontinuities in the dual unknown (multi-materials [41], solidification [16], biofilms [35], multi-phase flow [15], Stokes flow [47]), functions with discontinuous derivatives enhance the standard basis.”
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) (2011, background): “This enrichment function is suitable for any problem involving discontinuities in the first derivative of the solution such as diffusion problems arising in solidification [39] or biofilm growth [40].”
Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals (2010, unknown): “growing cracks, biofilms [20, 21] or hydrogels [22]).”
On three-dimensional modelling of crack growth using partition of unity methods (2010, background): “The equations can be solved on the same mesh as the mechanics problem, as in [61], or on a (possibly non-matching) finite difference mesh, as in [43,112].”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, background): “In addition, the extended finite element [20–26] has been proposed to solve the crack problem.”