  This paper proposes a volumetric penalty method to simulate the boundary
conditions for a non-linear hyperbolic problem. The boundary conditions are
assumed to be maximally strictly dissipative on a non-characteristic boundary.
This penalization appears to be quite natural since, after a natural change of
variable, the penalty matrix is an orthogonal projector. We prove the
convergence towards the solution of the wished hyperbolic problem and that this
convergence is sharp in the sense that it does not generate any boundary layer,
at any order. The proof involves an approximation by asymptotic expansion and
energy estimates in anisotropic Sobolev spaces.
