  We propose a new Nitsche-type approach for weak enforcement of normal
velocity boundary conditions for a Lagrangian discretization of the
compressible shock-hydrodynamics equations using high-order finite elements on
curved boundaries. Specifically, the variational formulation is appropriately
modified to enforce free-slip wall boundary conditions, without perturbing the
structure of the function spaces used to represent the solution, with a
considerable simplification with respect to traditional approaches. Total
energy is conserved and the resulting mass matrices are constant in time. The
robustness and accuracy of the proposed method are validated with an extensive
set of tests involving nontrivial curved boundaries.
