Chapter 9 - Finite-Volume Time Domain Method

Abstract

This chapter presents the finite-volume time domain (FVTD) method for the solution of Maxwell's equations. Initially, the FVTD method was developed as a numerical technique to solve the partial differential equations of hyperbolic conservation laws. The technique proved to be very successful in computational fluid dynamics, for solving the Euler and Navier–Stokes equations. The chapter describes the background of the finite-volume method, relevant to electromagnetic applications. Also, the finite-volume discretization of Maxwell's equations is elaborated in detail. A discussion of the stability of the method is also presented. The chapter extends the applicability of the finite-volume method in various ways by showing the way one can incorporate thin-wire models in the method. Also, a hybrid FVTD-FDTD method is presented that improves the performances of both the FVTD and the FDTD methods. Finally, another approach to the FVTD method is presented that can be viewed as a mixture of a conventional FVTD method and a generalization of the FDTD method. Examples computed with the techniques are presented and their results are compared to results obtained with other numerical methods or by measurement.