Simulation of unsteady turbulent flows around moving aerofoils using the pseudo-time method

The pseudo-time formulation of Jameson has facilitated the use of numerical methods for unsteady flows, these methods have proved successful for steady flows. The formulation uses iterations through pseudo-time to arrive at the next real time approximation. This iteration can be used in a straightforward manner to remove sequencing errors introduced when solving mean flow equations together with another set of differential equations (e.g. two-equation turbulence models or structural equations). The current paper discusses the accuracy and efficiency advantages of removing the sequencing error and the effect that building extra equations into the pseudo-time iteration has on its convergence characteristics. Test cases used are for the turbulent flow around pitching and ramping aerofoils. The performance of an implicit method for solving the pseudo-steady state problem is also assessed.