ANALYTIC VALIDATION OF A THREE-DIMENSIONAL SOLAR-POTENTIAL FINITE- DIFFERENCE CODE FOR LOW-FREQUENCY MAGNETIC INDUCTION

Abstract

This paper presents a detailed comparison of numerical and analytical calculations of the low-frequency electric and current density fields, induced by an applied uniform axial magnetic field, in an equatorially stratified sphere having the conductivity distribution Rho (_)=Rho0e- cos( _) with p {1,2} and > 0. As shown by the analytic solution, the resulting induced fields are fully three-dimensional, and the model therefore serves as a rigorous test of numerical codes The numerical method is a scalar-potential finite-difference scheme based on Stevenson's method for isolated conducting bodies. This computer code was recently shown to provide excellent agreement with results computed independently by a modified Finite-Difference Time-Domain method. Nevertheless, both codes share some underlying similarities, such as their common use of parallelepiped material voxels to represent the conductivity distribution, and of an edge-based staggered to model the electric fields. Therefore, it is of value to compare the numerical results with analytic ones The analytic model has a freely adjustable contrast parameter, and supports both pi and 2pi-periodic conductivity distributions. Numerical and analytical results are compared for several configurations. Full three-dimensional volumetric correlation coefficients are typically of the order of 99% or better. As might be expected, the main differences occur at the surface of the sphere, where the true circumferential fields are most poorly approximated by the staircasing approximation inherent the numerical approximation. [Vol. 11, No. 3 (1996), pp 72-81]