Improved efficiency for the numerical continuation of RANS equations

The numerical continuation of the Reynolds Averaged Navier-Stokes equations involves computation of the solution of large non-linear systems, resulting in high computational cost. Three different methods are implemented to reduce the computational cost of these calculations. Firstly, the turbulence model is decoupled from the main flow equations allowing two smaller systems to be solved. The Recursive Projection Method is implemented to allow existing time integration techniques to be used in the computation of unstable solutions. Finally, bifurcation tracking methods are presented that allow the bifurcation point to be tracked with two parameters without the need for multiple continuation runs. The decoupling method works up to parameter values close to the bifurcation point, where flow separation occurs and the cross-derivative terms in the Jacobian become more important. The Recursive Projection Method shows potential in extending the applicability of time integration methods by allowing them to converge onto unstable solutions. The bifurcation trackers successfully follow the Hopf bifurcation in multiple parameters allowing loci of bifurcations to be mapped in two parameter space. Results are shown for aerofoils at a range of transonic conditions.