The prediction of interaction phenomena between a compressible flow in a moving domain and other models like structural ones requires that some conservation properties need to be satisfied by the numerical schemes. In this paper we investigate the important problem of the work-energy conservation within the fluid for the discrete formulation on moving grids. In the case of a compressible flow, the work performed on the fluid by the moving interface has to be properly translated in a variation of the total fluid energy. We present a numerical model that satisfies this energy conservation property without loosing some other conservation properties such as the Geometric Conservation Law.