Traditionally, the design of the Horizontal Axis Wind Turbine (HAWT) has relied on momentum-based methods such as the Blade Element-Momentum (BEM) models. With the growth of computational power, optimization of wind turbines by using Computational Fluid Dynamics (CFD) for the explicit wake modelling is becoming more mainstream. Wake modelling is also conveniently handled by Lagrangian vortex methods, which offer the advantage of auto-adaptivity regarding multi-scale vortical flows and distribution of vorticity in space. The current thesis work focusses on the class of Vortex Particle Methods (VPM) which allows for the efficient treatment of complex wake aerodynamics, especially when the connectivity of vortex filaments plays a significant role, such as with blade-wake interactions and viscous or turbulent diffusion.