STABILITY OF METHODS IN THE FREE-VORTEX WAKE ANALYSIS OF WIND TURBINES

An analysis of the stability and accuracy of some timemarching methods used in the free-vortex wake analysis of wind turbines has been performed. Both linear and nonlinear stability analyses have been conducted. Integration schemes examined included the Euler explicit, Adams-Bashforth, and two predictor-corrector schemes. The linear stability analysis is shown to give an upper bound in determining the stability of each numerical method. However, it is further shown that the induced velocity term in the governing equations of the wake makes the overall stability problem nonlinear. A nonlinear stability analysis of the various schemes was performed using the method of modified equations. The numerical convergence of the wake was further examined following the methodology of conventional computational fluid dynamics. A predictor-corrector scheme with two time-step backward difference approximation was shown to be optimum when considering the overall stability, dispersion, and computational cost of each integration method. NOMENCLATURE Cl

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