  New entropy stable spectral collocations schemes of arbitrary order of
accuracy are developed for the unsteady 3-D Euler and Navier-Stokes equations
on dynamic unstructured grids. To take into account the grid motion and
deformation, we use an arbitrary Lagrangian-Eulerian (ALE) formulation. As a
result, moving and deforming hexahedral grid elements are individually mapped
onto a cube in the fixed reference system of coordinates. The proposed scheme
is constructed by using the skew-symmetric form of the Navier-Stokes equations,
which are discretized by using summation-by-parts spectral collocation
operators that preserve the conservation properties of the original governing
equations. Furthermore, the metric coefficients are approximated such that the
geometric conservation laws (GCL) are satisfied exactly on both static and
dynamic grids. To make the scheme entropy stable, a new entropy conservative
flux is derived for the 3-D Euler and Navier-Stokes equations on dynamic
unstructured grids. The new flux preserves the design order of accuracy of the
original spectral collocation scheme and guarantees the entropy conservation on
moving and deforming grids. We present numerical results demonstrating design
order of accuracy and freestream preservation properties of the new schemes for
both the Euler and Navier-Stokes equations on moving and deforming unstructured
grids.
