Numerical solutions of Laplace's equations and the ion current problem by the use of flux tubes and equipotentials (FTE)

Abstract

The method presented uses finite-difference and current-conservation equations, but applies them on a grid which is continuously adjusted by relaxation to approximate flux tube and equipotential surfaces. The resulting solution then contains the flux lines and equipotential lines explicitly. The primary advantages for using the method are that numerical diffusion of the ions is avoided, and the method is adaptable able to include physical diffusion terms.<>