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Mathematical Models and Computer Simulations

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01.11.2019

Variational Entropic Regularization of the Discontinuous Galerkin Method for Gasdynamic Equations

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 6/2019

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Abstract

A constructive version of the discontinuous Galerkin method (DGM) of arbitrary orders of accuracy to solve gasdynamic (GD) equations is proposed. This DGM 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.

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A. G. Kulikovsky, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Taylor Francis, London, 2000).

L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, 2nd ed. (Fizmatlit, Moscow, 2001; Butterworth-Heinemann, 1987).

S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, and G. P. Prokopov, Numerical Solution of Multidimensional Problems of Gas Dynamics (Nauka, Moscow, 1976) [in Russian].

B. Cockburn, “An introduction to the discontinuous Galerkin method for convection - dominated problems,” in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lect. Notes Math. 1697, 151–268 (1998).MATH

B. Cockburn, G. E. Karniadakis, and Ch.-W. Shu, “The development of discontinuous Galerkin methods,” IMA Preprint Ser. No. 1662 (Inst. Math. Appl., Univ. Minnisota, 1999).

B. Cockburn and Ch.-W. Shu, “Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems,” J. Sci. Comput. 16, 173–261 (2001).MathSciNetCrossRef

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, “Unified analysis of discontinuous Galerkin methods for elliptic problems,” SIAM J. Numer. Anal. 29, 1749–1779 (2002).MathSciNetCrossRef

M. E. Ladonkina, O. A. Neklyudova, and V. F. Tishkin, “Application of averaging to smooth the solution in DG method,” Preprint KIAM RAS No. 89 (Keldysh Inst. Appl. Math., Moscow, 2017).

M. E. Ladonkina, O. A. Neklyudova, and V. F. Tishkin, “Impact of different limiting functions on the order of solution obtained by RKDG,” Math. Model. Comput. Simul. 5, 346–349 (2013).MathSciNetCrossRef

10.

M. M. Krasnov, P. A. Kuchugov, M. E. Ladonkina, and V. F. Tishkin, “A generalization of the Godunov method using piecewise polynomial approximations in the multidimensional case,” in Supercomputing and Mathematical Modeling, Proceedings of the 16th International Conference, Oct. 3–7,2016, Ed. by R. M. Shagaliev (RFIATS-VNIIEF, Sarov, 2017), pp. 168-183.

11.

M. E. Ladonkina and V. F. Tishkin, “On Godunov type methods of high order of accuracy,” Dokl. Math. 91, 189–192 (2015).MathSciNetCrossRef

12.

V. F. Tishkin, V. T. Zhukov, and E. E. Myshetskaya, “Justification of Godunov’s scheme in the multidimensional case,” Math. Model. Comput. Simul. 8, 548–556 (2016).MathSciNetCrossRef

13.

P. G. le Floch, J. M. Mercier, and C. Rohde, “Fully discrete, entropy conservative schemes of arbitrary order,” SIAM J. Numer. Anal. 40, 1968–1992 (2002).MathSciNetCrossRef

14.

F. Lagoutiere, “A non-dissipative entropic scheme for convex scalar equations via discontinuous cell-reconstruction,” C. R. Math. 338, 549–554 (2004).MathSciNetCrossRef

15.

H. Zakerzadeh and U. S. Fjordholm, “High-order accurate, fully discrete entropy stable schemes for scalar conservation laws,” IMA J. Numer. Anal. 36, 633–654 (2016).MathSciNetCrossRef

16.

U. S. Fjordholm, R. Kappeli, S. Mishra, and E. Tadmor, “Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws,” Found. Comput. Math. 17, 763–827 (2017).MathSciNetCrossRef

17.

A. R. Winters and G. J. Gassner, “A comparison of two entropy stable discontinuous galerkin spectral element approximations for the shallow water equations with non-constant topography,” J. Comput. Phys. 301, 357–376 (2015).MathSciNetCrossRef

18.

G. J. Gassner, A. R. Winters, and D. A. Kopriva, “A well balanced and entropy conservative discontinuous galerkin spectral element method for the shallow water equations,” Appl. Math. Comput. 272, 291–308 (2016).MathSciNetMATH

19.

T. Chen and Ch.-W. Shu, “Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws,” J. Comput. Phys. 345, 427–461 (2017).MathSciNetCrossRef

20.

I. B. Petrov and A. S. Kholodov, “Regularization of discontinuous numerical solutions of equations of hyperbolic type,” USSR Comput. Math. Math. Phys. 24, 128–138 (1984).MathSciNetCrossRef

21.

Y. A. Kriksin and V. F. Tishkin, “Entropic regularization of discontinuous Galerkin method in one-dimensional problems of gas dynamics,” KIAM Preprint No. 100 (Keldysh Inst. Appl. Math., Moscow, 2018).

Titel: Variational Entropic Regularization of the Discontinuous Galerkin Method for Gasdynamic Equations
Publikationsdatum: 01.11.2019
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 6/2019
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048219060103

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