A new and novel GPU accelerated method has been developed for solving the Navier-Stokes equations for bodies of arbitrary geometry in both 2D and 3D. The present method utilises the vortex particles to discretize the governing equations in the Lagrangian frame. Those particles act as vorticity carriers which translate in accordance with the local velocity field. Vorticity information is thus propagated from the vorticity source to the rest of the flow domain in mimicking the advection and diffusion processes of the real flow.
In the high-fidelity method, vorticity generation can take place around the bodies. The no-slip condition produces a boundary flux which is subsequently diffused to the neighbouring particles. The new method has been successfully validated by simulating the flow field of an impulsively started cylinder. The calculated drag curve matches well with the theoretical prediction and other numerical results in the literature. To extend the applicability of the code to wind-turbine applications, a simplified re-meshing strategy is adopted which is found to produce small numerical inaccuracies.
In the engineering method, a simplified hybrid approach has been developed which decouples the advection and diffusion processes. The viscous effects are ignored on the bodies and are recovered in the wake. For this purpose, the Laplace equation that resulted from the irrotational assumption of the flow has been solved using the boundary element method. The solution produces a dipole distribution that is subsequently converted to viscous particles by employing the Hess’ equivalence principle. In addition, an accurate interpolation scheme has been developed to evaluate the dipole gradient across the distorted wake geometry.
To reduce the simulation time, the fast multipole method has been implemented on the GPU in 2D and 3D. To parallelize the implementation, a novel data construction algorithm has been proposed. Furthermore, an analytical expression for the velocity strain has been derived.
The new developed methods have been applied to problems involving aerofoils and vertical axis wind turbines. Comparisons with experimental data have shown that the new techniques are accurate and can be used with confidence for a wide variety of wind turbine applications
