We present an updated global model of the solar corona, including the transition region. We simulate the realistic three-dimensional (3D) magnetic field using the data from the photospheric magnetic field measurements and assume the magnetohydrodynamic (MHD) Alfvén wave turbulence and its nonlinear dissipation to be the only source for heating the coronal plasma and driving the solar wind. In closed-field regions, the dissipation efficiency in a balanced turbulence is enhanced. In the coronal holes, we account for a reflection of the outward-propagating waves, which is accompanied by the generation of weaker counterpropagating waves. The nonlinear cascade rate degrades in strongly imbalanced turbulence, thus resulting in colder coronal holes. The distinctive feature of the presented model is the description of the low corona as almost-steady-state low-beta plasma motion and heat flux transfer along the magnetic field lines. We trace the magnetic field lines through each grid point of the lower boundary of the global corona model, chosen at some heliocentric distance, R = Rb ∼ 1.1R⊙, well above the transition region. One can readily solve the plasma parameters along the magnetic field line from 1D equations for the plasma motion and heat transport together with the Alfvén wave propagation, which adequately describe the physics within the heliocentric distance range R⊙ < R < Rb, in the low solar corona. By interfacing this threaded-field-line model with the full MHD global corona model at r = Rb, we find the global solution and achieve a faster-than-real-time performance of the model on ∼200 cores.