In this paper, computations of transonic (M = 0.85) flow over an open cavity are performed through use of a high-order solver employing different Delayed Detached-Eddy Simulation (DDES) strategies: DDES, DDES with shear-layer-adapted subgrid length scale (DDES-SLA), and Improved DDES with SLA (IDDES-SLA). The cavity is considered to have no physical lateral walls, instead the computational domain inside the cavity is terminated in that direction by periodic or slip wall conditions. Different lateral domain sizes are studied. The length-to-depth ratio of the cavity is taken constant at 5 which matches that of the classical M219 cavity, and hence the simulated results are compared with available computational and experimental data for it. The results show that mean and turbulent flow fields at the midspan plane could be captured reasonably without lateral walls in the cavity, when the slip or periodic conditions are applied at least one depth separation. In addition, the use of the SLA length scale, which accelerates the transition to resolved turbulence in shear layers, helps capturing the Kelvin-Helmholtz instability dominated region, thereby providing better turbulent and acoustic related results than use of the standard one, i.e. the maximum cell dimension. Applying slip wall boundary condition at the lateral terminations of the cavity improves the velocity gradients over the periodic one, towards the aft wall which directly affects the sound levels emanating from the cavity ceiling. The best acoustic results are obtained by IDDES-SLA among all the tested, showing good agreement with those of the reference studies. The absence of viscous lateral walls in the cavity does not seem to have an impact on the sound levels except the region close to the front wall.