An adaptive multitime multigrid algorithm for time-periodic flow simulations

The multiscale behaviour and multidisciplinary nature of rotorcraft aerodynamics has delayed the introduction of CFD techniques for rotorcraft aerodynamics. The numerical dissipation of standard CFD algorithms may destroy tip vortices before blade–vortex interaction takes place. More advanced CFD algorithms, using high order discretization and/or local grid refinement, are better suited to tackle the problem. These algorithms, however, generally increase the computational complexity of the simulation and their efficiency should be improved before they can be applied to rotorcraft aerodynamics. In this paper, a four-dimensional solution algorithm will be presented which significantly improves the efficiency by exploiting the periodic nature of rotor flows.The efficiency of the algorithm is attained by changing a dynamic problem into a static problem, which simplifies the coupling with other models (blade dynamics and elastics, rotor trim), allows local grid refinement in space and time without dynamic load balancing issues, and solves a periodic problem by construction.A three-dimensional multigrid algorithm for DG discretisations on curvilinear structured meshes is extended to four-dimensional, curvilinear meshes with local grid refinement. Simulations for an oscillating airfoil in subsonic and transonic conditions confirm the performance of the multigrid algorithm and its insensitiveness to highly irregular grid features. The temporal stability restriction of the pseudo-time step is removed by treating the diagonal term of the time derivative implicitly.