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. 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.
Citation:
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Ensuring the entropy stability of the discontinuous Galerkin method in gas-dynamics problems”, Keldysh Institute preprints, 2019, 051, 22 pp.
\Bibitem{BraKriTis19}
\by M.~D.~Bragin, Yu.~A.~Kriksin, V.~F.~Tishkin
\paper Ensuring the entropy stability of the discontinuous Galerkin method in gas-dynamics problems
\jour Keldysh Institute preprints
\yr 2019
\papernumber 051
\totalpages 22
\mathnet{http://mi.mathnet.ru/ipmp2689}
\crossref{https://doi.org/10.20948/prepr-2019-51}
\elib{https://elibrary.ru/item.asp?id=37621679}
Linking options:
https://www.mathnet.ru/eng/ipmp2689
https://www.mathnet.ru/eng/ipmp/y2019/p51
This publication is cited in the following 7 articles:
O. R. Ragimli, Yu. A. Poveschenko, S. B. Popov, V. O. Podryga, P. I. Ragimli, “Dvukhsloinye polnostyu konservativnye skhemy gazovoi dinamiki s uzlovoi approksimatsiei i adaptivnoi regulyarizatsiei resheniya v peremennykh Eilera”, Preprinty IPM im. M. V. Keldysha, 2022, 008, 19 pp.
O. R. Rahimly, Yu. A. Poveshchenko, S. B. Popov, “Two-layer 1D completely conservative difference schemes of gas dynamics with adaptive regularization”, Math. Models Comput. Simul., 14:5 (2022), 771–782
Orkhan Rahimly, Yury Poveshchenko, Viktoriia Podryga, Parvin Rahimly, Lecture Notes in Computational Science and Engineering, 141, Mesh Methods for Boundary-Value Problems and Applications, 2022, 415
V. F. Masyagin, R. V. Zhalnin, M. E. Ladonkina, O. N. Terekhina, V. F. Tishkin, “Primenenie entropiinogo limitera dlya resheniya uravnenii gazovoi dinamiki s ispolzovaniem neyavnoi skhemy razryvnogo metoda Galerkina”, Preprinty IPM im. M. V. Keldysha, 2021, 007, 18 pp.
Victor F. Masyagin, Communications in Computer and Information Science, 1413, Mathematical Modeling and Supercomputer Technologies, 2021, 33
Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables”, Math. Models Comput. Simul., 13:3 (2021), 416–425
Yu. A. Kriksin, V. F. Tishkin, “Chislennoe reshenie zadachi Einfeldta na osnove razryvnogo metoda Galerkina”, Preprinty IPM im. M. V. Keldysha, 2019, 090, 22 pp.
Citation in format AMSBIB
Contact us: