Two Entropic Finite Volume Schemes for a Nernst–Planck–Poisson System with Ion Volume Constraints

Modeling and simulation of ion transport in electrolytes is an important tool to investigate electrochemical devices as well as biological systems at the cell scale. Well designed models follow first principles of non-equilibrium thermodynamics and include the fact that ions have a finite size. It is highly desirable that these properties are valid as well for discretized models. In this contribution, we present two numerical fluxes for two-point flux finite volume schemes which fulfill these requirements. We review recent results on entropic behavior and convergence. Concluding, we present first simulation results for biological ion channels.