We focuse on numerical simulation of two dimensional compressible fluids flows written in Lagrangian frame. Here, the initial mesh, generally formed by quadrangles (but triangles may sometimes appear), moves at speed of flows. Bad cells may come very quickly in regions of interacting shocks and/or very rarefaction. We present, on a simple exemple, the benefits of an Arbitrary Lagrangian-Eulerian formulation with respect to a pure Lagrangian step. The global scheme is obtained by a splitting procedure, the pure Lagrangian step is followed by a remeshing step. The last is it-self formed by a smoothing mesh process and by a projection that must be conservative. In the smooothing step, we describe an extension of Escobar et al. algorithm, we take into account the mesh connectivity (arbitrary), moreover we explain the ``nodal quality'' notion which permits to control the region where singularity may appears (non convex cells or the sinus of angles is to small, big volume variation of adjacent cells, etc..). In the second (projection) step, we expose a method that is free to compute the intersection between the Lagrangian and the smoothed mesh. This operation (for which only the same connectivity hypothesis holds) is a O(N) operation, where N is the total edges number. We will show numerical results on all the projected quantities : density, speed, and specific quantities.