This paper describes a methodology for the simulation of high Reynolds number flow over rigid and moving bodies. The calculations are performed on a structured Cartesian grid regardless of the geometric complexity or motion of the body. The approach is based on a modified version of the Brinkman Penalization method. The spatial derivatives of fluxes are discretized using a Weighted Essentially Non-Oscillatory (WENO) scheme. This paper describes a simple modified penalization method. For high Reynolds number viscous flows, a k-ω turbulence model is implemented. The methodology and its numerical implementation are described. Some simple flow examples are given to assess the accuracy of the technique. Results are then presented for high Reynolds number flow over a fixed and an oscillating airfoil and comparisons are made with experiment. Finally, a three-dimensional implementation of the method is demonstrated.