  The entropy conservative, curvilinear, nonconforming, p-refinement algorithm
for hyperbolic conservation laws of Del Rey Fernandez et al. (2019), is
extended from the compressible Euler equations to the compressible
Navier-Stokes equations. A simple and flexible coupling procedure with planar
interpolation operators between adjoining nonconforming elements is used.
Curvilinear volume metric terms are numerically approximated via a minimization
procedure and satisfy the discrete geometric conservation law conditions.
Distinct curvilinear surface metrics are used on the adjoining interfaces to
construct the interface coupling terms, thereby localizing the discrete
geometric conservation law constraints to each individual element. The
resulting scheme is entropy conservative/stable, element-wise conservative, and
freestream preserving. Viscous interface dissipation operators are developed
that retain the entropy stability of the base scheme. The accuracy and
stability properties of the resulting numerical scheme are shown to be
comparable to those of the original conforming scheme (achieving ~p+1
convergence) in the context of the viscous shock problem, the Taylor-Green
vortex problem at a Reynolds number of Re=1,600, and a subsonic turbulent flow
past a sphere at Re = 2,000.
