The numerical prediction of interaction phenomena between a compressible flow model with a moving domain and other physical models requires that the work performed on the fluid is properly translated into total fluid energy variation. We present a numerical model relying on an Arbitrary Lagrangian-Eulerian (ALE) unstructured vertex-centered finite volume that satisfies this condition together with the Geometric Conservation Law. We apply this numerical scheme to the solution of a 3D fluid-structure interaction problem. The results are contrasted with those obtained by the energy non-conservative counterpart.