Transport Models for Collective Dynamics in Biological Systems

Numerical Methods for Chemotaxis and Related Models

Alexander Kurganov

Tulane University
[SLIDES]

Chemotaxis is a movement of micro-organisms or cells towards the areas of high concentration of a certain chemical, which attracts the cells and may be either produced or consumed by them. Chemotaxis typically causes cell aggregation when the cell density develops a spiky structure. Chemotaxis can be modelled by a system of convection-diffusion-reaction PDEs whose solutions may have the same spiky structure, which is not so easy to accurately capture numerically. I will discuss several finite-volume and hybrid finite-volume-finite-difference methods, which are designed to achieve an ultimate goal of developing a highly accurate, stable and robust numerical method for chemotaxis models. The discussed methods have been applied to the classical Patlak-Keller-Segel model, its regularizations and extensions to the two-species case as well as to the coupled chemotaxis–?uid system. The talk is based on joint works with A. Chertock, Y. Epsteyn, K. Fellner, A. Lorz, M. Lukacova-Medvidova and P.A. Markowich.