An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

We formulate and analyze a new finite difference scheme for a shallow water model in the form of viscous Burgers-Poisson system with periodic boundary conditions. The proposed scheme belongs to a family of three-level linearized finite difference methods. It is proved to preserve both momentum and e...

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Autores principales:	Chayapa Darayon, Morrakot Khebchareon, Nattapol Ploymaklam
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	finite difference Burgers-Poisson system invariant-preserving convergence analysis numerical experiments Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/2e6828fe31d54511a303bec83f08bdf2
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spelling	oai:doaj.org-article:2e6828fe31d54511a303bec83f08bdf22021-11-25T17:17:13ZAn Invariant-Preserving Scheme for the Viscous Burgers-Poisson System10.3390/computation91101152079-3197https://doaj.org/article/2e6828fe31d54511a303bec83f08bdf22021-10-01T00:00:00Zhttps://www.mdpi.com/2079-3197/9/11/115https://doaj.org/toc/2079-3197We formulate and analyze a new finite difference scheme for a shallow water model in the form of viscous Burgers-Poisson system with periodic boundary conditions. The proposed scheme belongs to a family of three-level linearized finite difference methods. It is proved to preserve both momentum and energy in the discrete sense. In addition, we proved that the method converges uniformly and has second order of accuracy in space. The analysis given in this work is the first time a pointwise error estimation is done on a second-order finite difference operator applied to the Burgers-Poisson system. We validate our findings by performing various numerical simulations on both viscous and inviscous problems. These numerical examples show the efficacy of the proposed method and confirm the proven theoretical results.Chayapa DarayonMorrakot KhebchareonNattapol PloymaklamMDPI AGarticlefinite differenceBurgers-Poisson systeminvariant-preservingconvergence analysisnumerical experimentsElectronic computers. Computer scienceQA75.5-76.95ENComputation, Vol 9, Iss 115, p 115 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	finite difference Burgers-Poisson system invariant-preserving convergence analysis numerical experiments Electronic computers. Computer science QA75.5-76.95
spellingShingle	finite difference Burgers-Poisson system invariant-preserving convergence analysis numerical experiments Electronic computers. Computer science QA75.5-76.95 Chayapa Darayon Morrakot Khebchareon Nattapol Ploymaklam An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
description	We formulate and analyze a new finite difference scheme for a shallow water model in the form of viscous Burgers-Poisson system with periodic boundary conditions. The proposed scheme belongs to a family of three-level linearized finite difference methods. It is proved to preserve both momentum and energy in the discrete sense. In addition, we proved that the method converges uniformly and has second order of accuracy in space. The analysis given in this work is the first time a pointwise error estimation is done on a second-order finite difference operator applied to the Burgers-Poisson system. We validate our findings by performing various numerical simulations on both viscous and inviscous problems. These numerical examples show the efficacy of the proposed method and confirm the proven theoretical results.
format	article
author	Chayapa Darayon Morrakot Khebchareon Nattapol Ploymaklam
author_facet	Chayapa Darayon Morrakot Khebchareon Nattapol Ploymaklam
author_sort	Chayapa Darayon
title	An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
title_short	An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
title_full	An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
title_fullStr	An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
title_full_unstemmed	An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System
title_sort	invariant-preserving scheme for the viscous burgers-poisson system
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/2e6828fe31d54511a303bec83f08bdf2
work_keys_str_mv	AT chayapadarayon aninvariantpreservingschemefortheviscousburgerspoissonsystem AT morrakotkhebchareon aninvariantpreservingschemefortheviscousburgerspoissonsystem AT nattapolploymaklam aninvariantpreservingschemefortheviscousburgerspoissonsystem AT chayapadarayon invariantpreservingschemefortheviscousburgerspoissonsystem AT morrakotkhebchareon invariantpreservingschemefortheviscousburgerspoissonsystem AT nattapolploymaklam invariantpreservingschemefortheviscousburgerspoissonsystem
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An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

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