The main scope of this PhD thesis is the analysis of unsteady laminar and transitional suddenly expanded flows. For this reason Implicit Large Eddy Simulation (ILES) approach was used in combination with high order, high resolution numerical methods. The numerical methods examined are a 2nd order Monotonic Upwind Scheme for Scalar Conservation Laws (MUSCL) with Van Leer limiter, a high order (3rd) interpolation and a 5th order Weighted Essentially Non-Oscillatory scheme (WENO). First the numerical data for three low (steady state) Reynolds numbers and for two unsteady ( in the form of primary frequencies) were compared to the experimental data and were found in good agreement. A grid convergence study was undertaken for two Reynolds numbers demonstrating grid convergence and justifying the selection of the grid. The three numerical methods were evaluated for two Reynolds numbers showing good agreement for Reynolds number 412 and discrepancies at Reynolds number 900 between MUSCL and WENO with the MUSCL demonstrating a very dissipative behavior. The physical behavior of the flow in a wide range of Reynolds numbers were examined. For this range the flow behavior changed from steady to unsteady laminar and finally exhibiting localized transition to turbulence. The behavior of the main recirculation areas was described and the vortex shedding that occur there and how this change with the Reynolds number. The flow was observed to change from an unsteady quasi three dimensional flow at Reynolds number 412 to an increased transitional state with three dimensional vortical structures at Reynolds number 550. Kinetic energy spectra were calculated for the aforementioned range of Reynolds numbers. The primary frequencies are increasing with Reynolds number as expected. The slopes that were calculated for the inertial subrange revealed a trend. As the Reynolds number is increasing the slopes are decreasing approaching the value given by Kolmogorov -5/3
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