Reprint of: Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes

A large set of different numerical tests has been carried out in order to check the accuracy and the robustness of the new method for both smooth and discontinuous problems. In particular we have compared the results for a steady vortex in equilibrium solved with a standard conforming ALE method (without any rezoning technique) and with our new nonconforming ALE scheme, to show that the new nonconforming scheme is able to avoid mesh distortion in vortex flows even after very long simulation times.