Near-wall Reynolds stress modelling in rotating channel flows using elliptic relaxation

Over the past twenty-five years, there has been considerable research devoted to the development of Reynolds stress turbulence models. One particular research area is the development of representations for the pressure-strain correlation which reliably account for the effects of solid walls with complex geometries. This thesis is a theoretical and numerical study of a fairly recent method: elliptic relaxation.There are two challenges in using this method: (1) the determination of appropriate boundary conditions for the elliptic relaxation equations, and (2) the numerical implementation of those boundary conditions in non-Cartesian geometries. In this thesis, a set of 2D boundary conditions are derived via an asymptotic analysis of the Reynolds stress transport equations through the viscous sublayer. 1D and 2D finite volume numerical models to solve two elliptic relaxation models, the k-epsilon- vv model and a Reynolds stress version, are developed. These formulations are then used to compute the steady flow through stationary and rotating plane channels, and through a plane diffuser. The results are compared with benchmark direct numerical simulation and experimental data