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.

gasdynamic equations, the discontinuous Galerkin method, tilt limiter, entropic inequality

Mathematical problems and theory of numerical methods

Bragin Mikhail Dmitrievich,  ,  orcid.org/0000-0002-3990-9583,  KIAM RAS

Kriksin Yury Anatolievich,  ,  orcid.org/0000-0002-3840-4874,  KIAM RAS

Tishkin Vladimir Fedorovich,  ,  orcid.org/0000-0001-7295-7002,  KIAM RAS