We present a model of a direct-current glow discharge that self-consistently reproduces its full longitudinal structure and provides reliable estimates of main discharge parameters in all of its regions. The model is based on the fluid description of ions and bulk electrons and incorporates analytical formulation of non-local ionization and excitation sources induced by fast electrons. Spatial distributions of main discharge parameters obtained for the case of an extended glass tube filled with argon at 0.5 Torr show pronounced near-cathode regions-the cathode sheath, the negative glow and the Faraday dark space-as well as the autonomous positive column and the anode sheath. Formation of the second electric field reversal and the transitional region between the Faraday dark space and the positive column are revealed. This transitional region occupies a considerable fraction of the discharge tube length, over which the bulk electron temperature increases by more than an order of magnitude. Comparison of simulation results with those obtained with a 2D fluid model with the local energy approximation, as well as with experimental data taken from literature is presented. The model can be realised in most modern low-temperature plasma simulation software. The underlying physics and assumptions are discussed in detail.