Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
Modeling biofilm processes using the immersed boundary method
Journal of Computational Physics
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Reactive autophobic spreading of drops
Journal of Computational Physics
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)
Hi-index | 0.09 |
In this work we propose a new model to simulate biofilm structures (''finger-like'', as well as, compact structures) as a result of microbial growth in different environmental conditions. At the same time, the numerical method that we use in order to carry out the computational simulations is new to the biological community, as far as we know. The use of our model sheds light on the biological process of biofilm formation since it simulates some central issues of biofilm growth: the pattern formation of heterogeneous structures, such as finger-like structures, in a substrate-transport-limited regime, and the formation of more compact structures, in a growth-limited-regime. The main advantage of our approach is that we consider several of the most relevant aspects of biofilm modeling, particularly, the existence and evolution of a biofilm-liquid interface. At the same time, in order to perform numerical simulations, we have used sophisticated numerical techniques based on mixing the immersed interface method and the level-set method, which are well described in the present work.