Finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion

We propose and analyse two structure preserving finite volume schemes to approximate the solutions to a cross-diffusion system with self-consistent electric interactions introduced by Burger, Schlake & Wolfram (2012). This system has been derived thanks to probabilistic arguments and admits a thermodynamically motivated Lyapunov functional that is preserved by suitable two-point flux finite volume approximations. This allows to carry out the mathematical analysis of two schemes to be compared.

This is joint work with Maxime Herda and Annamaria Massimini.