Abstract
This paper is a review, with examples, of those areas where the theory of Fourier transforms has played a role in the development of computational methods in fluid and field dynamics. These may be separated into Ul the development of computing algorithms using Fourier transforms and the analysis of standard finite difference and finite element algorithms by Fourier methods. Recent results in the analysis of spurious reflection phenomena at computational boundaries of fluid flow simulation, which invoke the theory of wave propagation and the concept of group velocity, are given.