A new method to introduce constraints in cell-centered Lagrangian schemes

•We describe a new method to model constrained problems in the field of compressible hydrodynamics.•The method is adapted to cell-centered lagrangian schemes.•It is based on a minimization function over a specific set that models the constraints.•We prove that our method preserves the main physical properties such as momentum and total energy.•We illustrate our method with several numerical examples.

We describe a new method to introduce constraints in cell-centered Lagrangian schemes in the framework of compressible hydrodynamics. In this paper we apply it to the modeling of contact and sliding on solid wall boundaries. We illustrate our method, which is based on the minimization of a specific objective function, by several basic problems.