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Matem. Mod., 2021, Volume 33, Number 7, Pages 109–120 (Mi mm4307)  

Computational efficiency of ADER and RK schemes for discontinuous Galerkin method in case of 1D Hopf equation

I. S. Bosnyakovab, N. A. Klyueva

a Moscow Institute of physics and technology (MIPT)
b Central Aerohydrodynamic Institute named after prof. N.E. Zhukovsky (TsAGI)

Abstract: This paper considers Discontinuous Galerkin schemes based on Legendre polynomials of degree $K=2, 3$. Schemes are written to solve the one-dimensional Hopf equation. Unsteady solution is acquired with ADER and Runge-Kutta algorithms. The high order of numerical approaches is affirmed. The ADER method computational efficiency is studied in comparison with traditional approach. Tests that are used are with an analytical solution (linear solution and running half-wave), and with Burgers turbulence. The result of this work can be used to speed up 3D DG-based algorithms.

Keywords: discontinuous Galerkin method, Hopf equation, efficiency, ADER, Runge–Kutta, burgulence, high-order.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00163


DOI: https://doi.org/10.20948/mm-2021-07-08

Full text: PDF file (467 kB)
First page: PDF file
References: PDF file   HTML file

Received: 24.11.2020
Revised: 24.11.2020
Accepted:24.05.2021

Citation: I. S. Bosnyakov, N. A. Klyuev, “Computational efficiency of ADER and RK schemes for discontinuous Galerkin method in case of 1D Hopf equation”, Matem. Mod., 33:7 (2021), 109–120

Citation in format AMSBIB
\Bibitem{BosKly21}
\by I.~S.~Bosnyakov, N.~A.~Klyuev
\paper Computational efficiency of ADER and RK schemes for discontinuous Galerkin method in case of 1D Hopf equation
\jour Matem. Mod.
\yr 2021
\vol 33
\issue 7
\pages 109--120
\mathnet{http://mi.mathnet.ru/mm4307}
\crossref{https://doi.org/10.20948/mm-2021-07-08}


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