In recent years, the size and capacity of wind farms have increased significantly, as larger turbines are being clustered together to take advantage of the available wind resource. In large-scale wind farms, the downstream wind turbines will inevitably operate within the wake of the upstream ones. This leads to an apparent reduction of the power output of the downstream turbines and contributes towards increasing machine loads. Both effects limit the efficiency of a wind plant and therefore wake-turbine interactions are considered to be of significant engineering importance. This study focuses on developing and validating high-fidelity wind farm simulators for modelling wind farm wakes. Two approaches are presented: (1) a finite-element mesh-adaptive unsteady Reynolds-averaged Navier-Stokes (uRANS) solver and (2) a higher-order finite-difference turbulence-resolving solver. In both cases, the turbines are parametrised using a native actuator line model enhanced with turbine-level active control capabilities. The common denominator in the approaches is the significant speed-up and accuracy gain achieved by using non-standard numerical tools. The thesis provides detailed validation for the two models and examines their sensitivity to modeling parameters. First, via the mesh-adaptive uRANS simulations it is observed that the main parameter affecting the accuracy of the results is the edge-length of the underline mesh and that mesh-additivity only helps in reducing the number of elements (and therefore degrees of freedom) in the simulations. For the turbulence-resolving solver, a spectral vanishing viscosity (SVV) approach is used as an explicit subgrid-scale model. A new dynamic SVV model is developed which scales the local hyper viscosity afforded by the SVV operator, using the magnitude of the shear-rate tensor. This approach provides better results and is less sensitive to the selection of the SVV magnitude. Finally, the two models are also validated for large-scale wind farm simulations using data from utility-scale offshore wind farms.