This thesis has two topics : numerical methods for acoustic wave propagation in a flow and reduced order models. In the first topic, we develop a coupled finite element and boundary element method to solve the convected Helmholtz equation, when the flow is uniform outside a bounded domain. In particular, we propose a formulation that is well-posed at all the frequencies of the source. In the second topic, we propose a solution to the classical problem of round-off error accumulation that occurs when computing the a posteriori error bound in the reduced basis method. Furthermore, we propose a non intrusive method for the approximation, in a separated representation form, of linear systems resulting from the finite-dimensional approximation of boundary-value problems depending on one or several parameters
