In recent years, mathematical models of cell migration have become increasingly complex. These models have evolved from simple diffusion models to computationally troublesome reaction-diffusion-advection models. As such, the use of ``black box'' numerical solvers has become less appropriate. We discuss the application of the control volume technique for resolving a complicated nonlinear cell migration model. The nonlinearity is treated using an inexact Newton solver and flux limiting ensures that the cell migration fronts are captured adequately. Specifically, we analyse the model due to Perumpanani et al. (1999), comparing the numerical results of the proposed computational model developed in this research to previous results published by other researchers. We show that the finite volume computational model captures the physics of the processes with good accuracy using coarse meshes.
@article{930,
title = {Application of the control volume method to a mathematical model of cell migration},
journal = {ANZIAM Journal},
volume = {45},
year = {2004},
doi = {10.21914/anziamj.v45i0.930},
language = {EN},
url = {http://dml.mathdoc.fr/item/930}
}
Mallet, D. G.; Turner, I. W.; Pettet, G. J. Application of the control volume method to a mathematical model of cell migration. ANZIAM Journal, Tome 45 (2004) . doi : 10.21914/anziamj.v45i0.930. http://gdmltest.u-ga.fr/item/930/