A new Flow Simulation Methodology (FSM) is employed to investigate the wake behind axisymmetric bodies with a blunt base at supersonic speeds. The centerpiece of the FSM is a strategy to provide the proper amount of modelling of the subgrid scales. This is accomplished by a "contribution function" which locally and instantaneously compares the smallest relevant scales to the local grid size. The underlying compressible Navier-Stokes code in cylindrical coordinates employs high-order accurate finite differences and a high-order accurate axis treatment. The code also incorporates fully three-dimensional transport equations for turbulent kinetic energy and turbulent dissipation including compressible extensions and a state-of-the-art Reynolds stress model. FSM calculations are performed for M = 2.46 and ReD = 30,000 and are compared to DNS data obtained with essentially the same code. In addition, the FSM calculations are compared to steady RANS calculations using the standard K - ε model (STKE) and an explicit Algebraic Stress Model (ASM). Preliminary results for axisymmetric RANS calculations at M = 2.46 and ReD = 3,300,000 are shown. For this Reynolds number, the focus was on testing the turbulence model that would later be used for FSM calculations.