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KIAM Preprint  51, Moscow, 2019
Authors: Bragin M.D., Kriksin Y.A., Tishkin V.F.
Ensuring the entropy stability of the discontinuous Galerkin method in gas-dynamics problems
Abstract:
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. 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.
Keywords:
gasdynamic equations, the discontinuous Galerkin method, tilt limiter, entropic inequality
Publication language: russian,  pages: 22
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Bragin Mikhail Dmitrievich,  orcid.org/0000-0002-3990-9583KIAM RAS
  • Kriksin Yury Anatolievich,  orcid.org/0000-0002-3840-4874KIAM RAS
  • Tishkin Vladimir Fedorovich,  orcid.org/0000-0001-7295-7002KIAM RAS