A one-mesh method for the cell-centered discretization of slide lines

A new method is described to handle slide lines in cell-centered Lagrangian schemes for the modeling of sliding problems between two fluids in the framework of compressible hy- drodynamics. The method is an extension of the one proposed in the reference [1] and is conservative in momentum and total energy. Our method is based on the minimization of an objective function over a specific set that models the sliding constraint. We illustrate on several basic problems.