Application of Dual Time Stepping to Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge-Kutta schemes. In particular the method is applied to Gauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes (URANS) equations. It is concluded that the Radau 2A schemes are more robust and less computationally expensive because they require a much smaller number of inner iterations. Moreover these schemes seem to be competitive with alternative implicit schemes. I