Title :
Numerical solutions of Laplace´s equation and ion current flow by the use of flux-tube/equipotential relaxation
Author :
Lawless, Phil A.
Author_Institution :
Res. Triangle Inst., Research Triangle Park, NC, USA
Abstract :
A flux-tube/equipotential relaxation method has been developed for solving the Poisson equation for mobile ions. The method uses finite-difference and current conservation equations but applies them on a grid that is continuously adjusted by relaxation to approximate flux tube and equipotential surfaces. The solution represents the flux lines and equipotential lines and the electric field values on them. The advantages of the method are that free boundary problems can be solved naturally, numerical diffusion of the ions is avoided, and the method can include physical diffusion terms.<>
Keywords :
boundary-value problems; difference equations; electrostatics; Laplace´s equation; Poisson equation; current conservation equations; electric field; electrostatic; finite difference equations; flux-tube/equipotential relaxation; free boundary problems; ion current flow; mobile ions; physical diffusion; Computational modeling; Electrodes; Electrostatics; Finite difference methods; Finite element methods; Grid computing; Laplace equations; Poisson equations; Space charge; Voltage;
Conference_Titel :
Industry Applications Society Annual Meeting, 1989., Conference Record of the 1989 IEEE
Conference_Location :
San Diego, CA, USA
DOI :
10.1109/IAS.1989.96915
