A Power-law Preconditioning Approach for Accelerating the Convergence Rate of Steady and Unsteady Incompressible Turbulent Flows

In the present study, for the first time, the locally power-law preconditioning method for analyzing steady and unsteady incompressible turbulent flows around airfoils in high Reynolds numbers is utilized. In this method, the governing equations are modified by altering the time derivatives terms. The governing equations are discretized by the numerical method derived from the cell-centered Jameson’s finite volume algorithm. In addition, for solving the unsteady flows, an implicit dual-time procedure and for simulating the turbulent flows, Baldwin and Lomax algebraic model have been employed. The computations are presented for steady and unsteady turbulent flows around NACA0012 and ONERA-A airfoils at various angles of attack and Reynolds number. Results presented in the paper focus on the velocity, pressure and eddy viscosity profiles, distribution of pressure coefficient, lift and drag coefficients and the effect of the power-law preconditioning method on the convergence rate. The numerical solution indicates an acceptable accuracy with the aid of the power-law preconditioning method in both steady and unsteady turbulent flows for high Reynolds numbers. Moreover, using the power-law preconditioning method improves the convergence speed significantly and reduces the iteration number of solution steps and central processing unit time simultaneously in both steady and unsteady flows.