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Two distinct simulation methodologies: Delayed Detached Eddy Simulation (DDES) and stress based Wall-modelled Large Eddy Simulation (WMLES) are evaluated using structured overset curvilinear grids for the NASA juncture flow model. While both methodologies are shown to mitigate the primary shortcomings of steady state Reynolds Averaged Navier Stokes(RANS) simulations, several unresolved aspects are identified. Strong sensitivity to RANS-typegrid refinement is observed in the DDES with a substantial deterioration of the solution quality with increasing spatial resolution associated with deficiencies in the shielding function. Mean profiles for attached boundary layers on the fuselage show spurious inflections suggesting modelled stress depletion on finer grids. Lower numerical dissipation in terms of spatial discretization and time step size is seen to improve the solution quality, and the advantage of using RC and QCR2000 corrections in the underlying RANS closure is demonstrated for DDES on RANS-type meshes. Equilibrium Wall-Modelled LES used grids that resolved the tripping dots over the fuselage nose and the wing leading edge, consistent with the experiment setup. These simulations resulted in a cost-competitive approach compared to DDES on RANS-type grids. Although the agreement between WMLES predictions of first and second order single point statistics with experimental measurements is promising, a fundamental shortcoming is noted in terms of an overshoot in streamwise momentum in corner regions of the wing-fuselage juncture. This excess momentum subsequently delays the onset of separation,thereby resulting in an underprediction in length of the separation bubble. Some quantitative sensitivity to numerical discretization is observed; lowering of numerical dissipation shows better agreement with the experiment.