Flow simulation in channels with distorted geometry using a spectral code with co-ordinate transformations

Turbulence is essentially four-dimensional in character, and requires the corresponding treatment of the well-known Navier-Stokes equations. However, this has only been possible over the past twenty years and then by using the largest computers available. Interest is now turning from the initial, mainly smooth channel, simulations to geometries of eventual engineering significance. This paper reports a new code using the spectral methods of Orszag, but also incorporating a novel generalized co-ordinate transformation approach. Initial predictions for smooth channels agree well with published data. For distorted geometries, the initial velocity field has considerable influence on the success of the simulations. This is accommodated by gradual (step) changes towards the required distortion, so that the initial velocity field for the 'new' geometry is the final field from the previous step. Examples are given of different two-dimensional channel geometries achieved, and these include the successful prediction of recirculating flows.