Three-dimensional numerical simulation of ion nanochannels

In this article we deal with the three-dimensional (3D) simulation of biological nanochannels using the Galerkin Finite Element method. The mathematical problem is constituted by the coupled solution of the Poisson-Nernst-Planck equation system for ion electrodiffusion and of the Stokes equation system for electrolyte fluid motion. The Implicit Euler scheme and a Gummel type iteration are used for time advancing and problem decoupling, respectively, while a primal-mixed exponentially fitted finite element method on 3D simplices is adopted for discretization. Model and method validation is conducted on a series of benchmark problems previously studied in one and two spatial dimensions. Deviations between the 3D simulation and the corresponding lower-dimensional counterparts are then examined and physically investigated.