The work presents results of the application of a new OpenFOAM® solver QGDFoam for the numerical simulation of viscous compressible flows in a wide range of Mach numbers. The new solver is based on the explicit approximation of regularized, or quasi-gas dynamic (QGD) equations. The mixed finite-volume and finite-difference approximation is constructed on unstructured spatial grids with co-located variables storage. The solver has been tested for a number of 1D Riemann problems (Sod’s problem, Noh test and others) and 2D cases (Mach 3 forward step, Ladenburg supersonic jet flow with Mach reflection, NASA Langley supersonic overexpanded jet flow and subsonic laminar flow over a backward-facing step). Results of numerical simulations were compared with analytic solutions and OpenFOAM® implementation of the Kurganov-Tadmor scheme, known as rhoCentralFoam. The testing procedure has shown that whereas QGD algorithm is more diffusive than Godunov-type methods with 2nd order TVD schemes with limiters, it is far less diffusive compared with pure upwind schemes as HLL. It was shown that OpenFOAM implementation of the QGD algorithm allows to compute successfully subsonic, sonic and supersonic flows, while other OpenFOAM® solvers have a very limited operational Mach number range. Preliminary results of QGDFoam application for large-scale 3D problems are presented. Scaling tests for up to 768 cores showed good scalability of QGDFoam solver.