Three-dimensional numerical simulations of the flow around the NACA 0015 airfoil were conducted by using the unsteady Reynolds-averaged Navier-Stokes (URANS) and improved delayed detached eddy simulation (IDDES) based on k-ω shear stress transport (SST) turbulence model. The angle of attack range (AoA) is from 0° to 75°. The solver in this paper is developed on an in-house platform HRAPIF based on the finite volume method (FVM) with the elemental velocity vector transformation (EVVT) approach. It uses a density-based method with a low Mach preconditioning technique to accelerate convergence. The inviscid spatial discretization is the 5th-order modified weighted essentially non-oscillatory (WENO-Z) scheme. The results show that the IDDES model can effectively predict lift and drag coefficients at all the studied AoAs and has significant advantages over URANS, both in predicting aerodynamic forces and in simulating flow vortex structures at post-stall AoAs.