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The challenges encountered in computational analysis of wind turbines and turbomachinery include turbulent rotational ows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the uid structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The Arbitrary Lagrangian Eulerian (ALE) and Space Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization have been e ective in addressing these challenges. The ALE-VMS and ST-VMS serve as core computational methods. They are supplemented with special methods like the Slip Interface (SI) method and ST Isogeometric Analysis with NURBS basis functions in time. We describe the core and special methods and present, as examples of challenging computations performed, computational analysis of horizontaland vertical-axis wind turbines and ow-driven string dynamics in pumps.

Wind Turbine and Turbomachinery Computational Analysis with the ALE and Space-Time Variational Multiscale Methods and Isogeometric Discretization