A Detailed Examination of the Finite-Volume Time-Domain Method for Maxwell's Equations - Abstract

Author： Young J.L. Nelson R.O. Gaitonde D.V.

ISSN： 1569-3937

Source： Journal of Electromagnetic Waves and Applications, Vol.14, Iss.6, 2000-01, pp. : 765-766

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Abstract

A detailed analysis of the finite-volume, time-domain scheme, as applied to Maxwell's equations is provided herein. To accomplish the temporal discretization, the classical four-stage Runge-Kutta integrator is invoked. For the spatial discretization, this analysis articulates the role of the primitive vector in the reconstruction of flux quantities at boundary surfaces from cell average values. The accuracy of the spatial discretization scheme is directly tied to the accuracy of the discretization of the primitive vector's derivative. To realize a stable scheme, central, forward and backward differences may be invoked (the stencils may be explicit or implicit). However, for the latter two, a stable scheme is accomplished only if the fluxes are split in the direction of the outwardly pointing normal from a cell surface. For numerical examples, we consider third-order windward biased stencils; examples are given to demonstrate many of the key attributes and deficiencies of the method.