Non-oscillatory entropy stable DG schemes for hyperbolic conservation law

Fuente: arXiv
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Main Authors: Liu, Yuchang, Guo, Wei, Jiang, Yan, Zhang, Mengping
Format: Preprint
Published: 2024
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author Liu, Yuchang
Guo, Wei
Jiang, Yan
Zhang, Mengping
author_facet Liu, Yuchang
Guo, Wei
Jiang, Yan
Zhang, Mengping
contents In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integration factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.
format Preprint
id arxiv_https___arxiv_org_abs_2410_16729
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Non-oscillatory entropy stable DG schemes for hyperbolic conservation law
Liu, Yuchang
Guo, Wei
Jiang, Yan
Zhang, Mengping
Numerical Analysis
In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly controls entropy production and suppresses spurious oscillations. To address the stiffness introduced by the artificial terms, which can restrict severely time step sizes, we employ the integration factor strong stability-preserving Runge-Kutta method for time discretization. Furthermore, our method remains compatible with positivity-preserving limiters under suitable CFL conditions in extreme cases. Various numerical examples demonstrate the efficiency of the proposed scheme, showing that it maintains high-order accuracy in smooth regions and avoids spurious oscillations near discontinuities.
title Non-oscillatory entropy stable DG schemes for hyperbolic conservation law
topic Numerical Analysis
url https://arxiv.org/abs/2410.16729