  This article aims at developing a high order pressure-based solver for the
solution of the 3D compressible Navier-Stokes system at all Mach numbers. We
propose a cell-centered discretization of the governing equations that splits
the fluxes into a fast and a slow scale part, that are treated implicitly and
explicitly, respectively. A novel semi-implicit discretization is proposed for
the kinetic energy as well as the enthalpy fluxes in the energy equation, hence
avoiding any need of iterative solvers. The implicit discretization yields an
elliptic equation on the pressure that can be solved for both ideal gas and
general equation of state (EOS). A nested Newton method is used to solve the
mildly nonlinear system for the pressure in case of nonlinear EOS. High order
in time is granted by implicit-explicit (IMEX) time stepping, whereas a novel
CWENO technique efficiently implemented in a dimension-by-dimension manner is
developed for achieving high order in space for the discretization of explicit
convective and viscous fluxes. A quadrature-free finite volume solver is then
derived for the high order approximation of numerical fluxes. Central schemes
with no dissipation of suitable order of accuracy are finally employed for the
numerical approximation of the implicit terms. Consequently, the CFL-type
stability condition on the maximum admissible time step is based only on the
fluid velocity and not on the sound speed, so that the novel schemes work
uniformly for all Mach numbers. Convergence and robustness of the proposed
method are assessed through a wide set of benchmark problems involving low and
high Mach number regimes, as well as inviscid and viscous flows.
