We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions
for generic forms of equations of state, shear stress tensor and heat flux. With
this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta
time discretizations satisfy a weak positivity property. With a simple and effi-
cient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes
are rendered preserving the positivity of density and internal energy without los-
ing local conservation or high order accuracy. Numerical tests suggest that the
positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes
without other limiters can produce satisfying non-oscillatory solutions when
the nonlinear diffusion in compressible Navier-Stokes equations is accurately
resolved.