Abstract:
A constructive version of an arbitrary accuracy discontinuous Galerkin (DG) method solving gas dynamics equations is proposed. This DG method is based on the new variational principle of entropic regularization ensuring the implementation of discrete analogs of the conservation laws of mass, momentum, total energy and entropic inequality.
Citation:
Y. A. Kriksin, V. F. Tishkin, “Variational entropic regularization of discontinuous Galerkin method for gas dynamics equations”, Mat. Model., 31:5 (2019), 69–84; Math. Models Comput. Simul., 11:6 (2019), 1032–1040
This publication is cited in the following 12 articles:
I. M. Kulikov, “Using piecewise parabolic reconstruction of physical variables in Rusanov’s solver. II. Special relativistic magnetohydrodynamics equations”, J. Appl. Industr. Math., 18:1 (2024), 81–92
I. M. Kulikov, “Using piecewise parabolic reconstruction of physical variables in the Rusanov solver. I. The special relativistic hydrodynamics equations”, J. Appl. Industr. Math., 17:4 (2023), 737–749
I. M. Kulikov, D. A. Karavaev, “Using a Low Dissipation Lax–Friedrichs Scheme for Numerical Modeling of Relativistic Flows”, Numer. Analys. Appl., 16:4 (2023), 326
I. M. Kulikov, D. A. Karavaev, “A Piecewise-Parabolic Reconstruction of the Physical Variables in a Low-Dissipation HLL Method for the Numerical Solution of the Equations of Special Relativistic Hydrodynamics”, Numer. Analys. Appl., 16:1 (2023), 45
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.
I. M. Kulikov, “A Piecewise-Linear Reconstruction to Reduce the Dissipation of the HLL Method in Solving the Gas Dynamics Equations”, Numer. Analys. Appl., 15:2 (2022), 112
Igor Kulikov, Igor Chernykh, Dmitry Karavaev, Vladimir Prigarin, Anna Sapetina, Ivan Ulyanichev, Oleg Zavyalov, “A New Parallel Code Based on a Simple Piecewise Parabolic Method for Numerical Modeling of Colliding Flows in Relativistic Hydrodynamics”, Mathematics, 10:11 (2022), 1865
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
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
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.
R. V. Zhalnin, V. F. Masyagin, E. E. Peskova, V. F. Tishkin, “Primenenie razryvnogo metoda Galerkina k modelirovaniyu dvumernykh techenii mnogokomponentnoi smesi idealnykh gazov na adaptivnykh lokalno izmelchayuschikhsya setkakh”, Zhurnal SVMO, 21:2 (2019), 244–258
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