A preconditioned multigrid for simulation of atmospheric flow and wind turbine wakes

This paper demonstrates a low Mach number preconditioning formulation for high Reynolds number, low Mach number atmospheric flows. The preconditioning is implemented together with multigrid approach into a multistage solver in order to provide an efficient and robust all purpose solver to be used for the simulation of high Reynolds number viscous flows. Several modification and scaling of the preconditioned parameter are introduced to ensure robust use of the scheme for this particular flow regime in presence of stagnation points and seperation regions. The simulations results of standard cases of atmospheric flow over hilly terrain with attached and separated flow are presented to demonstrate the superior convergence, accuracy and robustness of the developed preconditioned scheme. An immersed wind turbine model is also developed and embedded into the preconditioned solver which allows for the simulations of far wake behind wind turbines in wind farms. The use of the immersed model reduces the stringent grid requirements of full RANS simulations around wind turbines and allows one to efficiently predict the wake evolution within wind farms.