Ensuring the entropy stability of the discontinuous Galerkin method in gas-dynamics problems

A new variational principle for deriving the discontinuous Galerkin method modified equations is proposed for solving one-dimensional equations of ideal gas dynamics, based, in particular, on the implementation of a discrete analogue of entropic inequality. А special entropic tilt limiter has been developed in connection with the proposed principle, which ensures non-negative entropy production in each finite element. Numerical calculations of some model problems have been carried out in order to evaluate the efficiency of the method.