Physics Preserving Discretizations for the Poisson-Nernst-Planck Equations

The system consisting of the Poisson equation coupled with the Nernst-Planck equations is a flexible model of the motion of electrically charged particles. It has a very slight nonlinearity which causes the system to be very sensitive to changes in certain parameters. Because of this, great care must be taken when discretizing the equations for numerical solution. This talk will present discretizations of the 1D Poisson-Nernst-Planck equations which preserve global conservation of mass or which preserve an energy dissipation law, and compare the solutions obtained from these discretizations to solutions obtained from standard discretizations.

Event Topic

Stochastic & Multiscale Modeling and Computation