GPU-enabled high-order gas-kinetic scheme for actuator line model simulations of wind turbine wakes

For the first time, we integrate the actuator line model (ALM) into a fourth-order gas-kinetic scheme (GKS) to accurately simulate wind turbine wakes. We first extend the GKS to the simulation of weakly compressible flows within a well-developed two-stage fourth-order framework. The ALM is included as an external body force term in the momentum equation for the GKS. The in-house second-order and fourth-order GKS with ALM is implemented on Graphics Processing Units (GPU) to leverage their parallel computing capabilities for wake turbulence simulation. The NREL 5 MW reference wind turbine is simulated using the GPU-enabled second-order and fourth-order GKS with ALM. The normal and tangential forces acting on the turbine blades agree well between the second-order and fourth-order GKS, indicating that the numerical discretization error has a very limited impact on the blade force predictions. For the wind turbine wake, the instantaneous wake turbulent structures, the time-averaged velocity and turbulent kinetic energy from the second-order GKS with locally-refined grids converge to those from the fourth-order GKS with uniform grids, demonstrating that the high-order numerical scheme improves the resolution of the vortex-dominated wake turbulence. In addition, the fourth-order GKS with uniform grid is more efficient than the second-order GKS with locally-refined grid.