  Non-linear entropy stability and a summation-by-parts framework are used to
derive entropy stable wall boundary conditions for the three-dimensional
compressible Navier--Stokes equations. A semi-discrete entropy estimate for the
entire domain is achieved when the new boundary conditions are coupled with an
entropy stable discrete interior operator. The data at the boundary are weakly
imposed using a penalty flux approach and a simultaneous-approximation-term
penalty technique. Although discontinuous spectral collocation operators on
unstructured grids are used herein for the purpose of demonstrating their
robustness and efficacy, the new boundary conditions are compatible with any
diagonal norm summation-by-parts spatial operator, including finite element,
finite difference, finite volume, discontinuous Galerkin, and flux
reconstruction/correction procedure via reconstruction schemes. The proposed
boundary treatment is tested for three-dimensional subsonic and supersonic
flows. The numerical computations corroborate the non-linear stability (entropy
stability) and accuracy of the boundary conditions.
