  In numerical simulations a smooth domain occupied by a fluid has to be
approximated by a computational domain that typically does not coincide with a
physical domain. Consequently, in order to study convergence and error
estimates of a numerical method domain-related discretization errors, the
so-called variational crimes, need to be taken into account. In this paper we
present an elegant alternative to a direct, but rather technical, analysis of
variational crimes by means of the penalty approach. We embed the physical
domain into a large enough cubed domain and study the convergence of a finite
volume method for the corresponding domain-penalized problem. We show that
numerical solutions of the penalized problem converge to a generalized, the
so-called dissipative weak, solution of the original problem. If a strong
solution exists, the dissipative weak solution emanating from the same initial
data coincides with the strong solution. In this case, we apply a novel tool of
the relative energy and derive the error estimates between the numerical
solution and the strong solution. Extensive numerical experiments that confirm
theoretical results are presented.
