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We study various formulations of the boundary conditions for the Euler equations of gas dynamics from a mathematical and numerical point of view. In the case of one space dimension, we recall the classical results, based on an analysis of the linearized problem. Then we present a more recent formulation of the problem, which allows for nonlinear effects at the boundary of the study domain. This formulation fits naturally into a finite volume discretization, and we present a significant one-dimensional test case.

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