Wind turbine wake computation with the ST-VMS method and isogeometric discretization: Directional preference in spatial refinement

In this sequel to a two-part article on wind turbine wake computation with the Space–Time Variational Multiscale (ST-VMS) method and ST isogeometric discretization, we study directional preference in spatial refinement. We evaluate the wake computation accuracy of different combinations of mesh resolutions in the free-stream and cross-flow directions. We also evaluate the accuracy of different combinations of B-spline polynomial orders in those directions. The computational framework is the same as in the two-part article. It is made of, in addition to the ST-VMS and ST isogeometric discretization, the Multidomain Method (MDM). It enables accurate representation of the turbine long-wake vortex patterns in a computationally efficient way. Because of the ST context, the computational framework has higher-order accuracy to begin with; because of the VMS feature, it addresses the computational challenges associated with the multiscale nature of the flow; with the isogeometric discretization, it provides increased accuracy in the flow solution; and with the MDM, a long wake can be computed over a sequence of subdomains, instead of a single, long domain, thus reducing the computational cost. Also with the MDM, the computation over a downstream subdomain can start several turbine rotations after the computation over the upstream subdomain starts, thus reducing the computational cost even more. In the computations presented here, as in the two-part article, the velocity data on the inflow plane comes from a previous wind turbine computation, extracted by projection from a plane located 10 m downstream of the turbine, which has a diameter of 126 m. The directional-refinement studies involve four different spatial resolutions, two different B-spline polynomial orders, and two different temporal resolutions. The studies show that there is some preference for refinement in the cross-flow directions.