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

fYear

1989

fDate

1-5 Oct. 1989

Firstpage

1999

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Industry Applications Society Annual Meeting, 1989., Conference Record of the 1989 IEEE

Conference_Location

San Diego, CA, USA

Type

conf

DOI

10.1109/IAS.1989.96915

Filename

96915