Multigrid acceleration of an upwind Euler method for hovering rotor flows

Abstract

The effect of multigrid acceleration implemented within an upwind-biased Euler method for hovering rotor flows is presented. The requirement to capture the vortical wake development over several turns means a long numerical integration time is required for hovering rotors, and the solution (wake) away from the blade is significant. Furthermore, the flow in the region near the blade root is effectively incompressible. Hence, the solution evolution and convergence is different to a fixed wing case where convergence depends primarily on propagating errors away from the surface as quickly as possible, and multigrid acceleration is shown to be less effective for hovering rotor flows. It is found that a simple V-cycle is the most effective, smoothing in the decreasing mesh density direction only, with a relaxed trilinear prolongation operator. Results are presented for multigrid computations with 2, 3, 4, and 5 mesh levels, and a CPU reduction of approximately 80% is demonstrated for five mesh levels.