Simulations of the flow over a generic fighter-airplane configuration are presented and analyzed in detail. Grid adaptation is essential to limit the errors, which interfere with physical reasoning, although true grid convergence is still out of reach. Turbulence is treated with two conventional RANS models, one of which is based on the Reynolds stresses (RSTM), and by a hybrid RANS-LES approach called DDES which resolves the turbulence activity, to the extent allowed by the grid, outside the boundary layers. A central difficulty of this fighter triple-delta wing is the axial flow in the various overwing vortices, which can be of jet-type or wake-type, and switch abruptly along a vortex. The associated pressure changes in some cases reverse the rolling moment on the airplane, at a high angle of attack with side-slip; this is an important design criterion. Comparisons with experimental field measurements are included, and generally favor DDES although it depends on the angles of attack and side-slip, and on which wing is considered. A rigorous post-processing system gives the budget of the Reynolds stresses following leading-edge separation, roll-up of the shear layer, and maturation of the vortices. This system incorporates the time-averaged effects of the sub-grid-scale terms, which appears to be a new and nontrivial step, and the sum of the terms approaches 0, which is not easy to achieve because energy conservation is not exact in simulations. This knowledge is expected to guide future RANS-model improvements, both of the eddy-viscosity and Reynolds-stress type.