On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems Ii: Entropy Bounded Formulations for Nonlinear Conservation Laws

We derive entropy conserving and dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The formulation imposes two-way coupling at the artificial interface boundaries through penalty functions that vanish when solutions coincide. are expressed terms fluxes originally introduced finite volume schemes. Entropy dissipation additional overlap region added use linear penalties.