Numerical simulation of dynamic stall using an improved advection upwind splitting method

In this study a dual-time integration method with the advection upwind splitting method based on flux difference (AUSMD) scheme is demonstrated with simplicity, robustness, and accuracy in solving the time-dependent full Navier-Stoke equations for aerodynamic analysis of stationary and oscillating airfoils. A pseudotime is introduced as an iteration strategy so that time accuracy for solving the unsteady equations can be preserved for long time. A second-order, time-accurate, Euler backward implicit discretization is made at the physical time level. A two-stage Runge-Kutta scheme is used in the pseudotime iteration, in combination with acceleration enhancement procedures, the local time stepping, and residual smoothing. The recent AUSMD flux scheme with a slight modification is applied for approximating the inviscid terms. This modification has been found necessary to provide robust and accurate solutions for the study of dynamic stall. Meanwhile, the renormalization group theory model is chosen to evaluate the turbulence eddy viscosity. Both light and deep dynamic stall cases were calculated, along with grid refinement and time-stepping size studies. Results of unsteady airload hysteresis curves and instantaneous flow pictures are analyzed and compared with measured data.

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