Efficient Flow Computation including Turbulent Transport

Abstract

Runge-Kutta/Implicit methods for the solution of the Navier-Stokes equations provide superior convergence rates, especially when combined with a multigrid framework. In previous investigations [7,8,10], the algebraic model of Baldwin and Lomax [1] was employed as turbulence model. In the present contribution, this model is replaced by the model of Spalart and Allmaras [9], where an additional partial differential equation has to be solved. The design of an appropriate solution strategy to solve this additional equation and account for the necessary coupling to the system of main flow equations to maintain the favorable convergence rates of the basic scheme are outlined and discussed. Different cases of turbulent subsonic and transonic flow around airfoils are considered to assess the convergence properties of the resulting algorithm. Comparison with results of previous investigations confirms that the high efficiency of the basic Runge-Kutta/Implicit method is not impaired when adding an equation for turbulent transport.