A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property

In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a se...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2019-02
Hauptverfasser: Li, Maojun, Xu, Liwei, Cheng, Yongping
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Li, Maojun
Xu, Liwei
Cheng, Yongping
description In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests.
doi_str_mv 10.48550/arxiv.1902.05688
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1902_05688</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2182958498</sourcerecordid><originalsourceid>FETCH-LOGICAL-a528-a6d40e0588948b079faae4e0867e92ae0184b7104c4270141ddc8e6904208b263</originalsourceid><addsrcrecordid>eNotkEFPAjEUhBsTEwnyAzzZxPPia7fdfT0ShNWE6IX7WujDLWF3sV1A_r0reJo5fJnMDGMPAsYKtYZnG378cSwMyDHoDPGGDWSaigSVlHdsFOMWAGSWS63TAfuc8OlLkcxnvKauah3ftIF3FfHu1CbO19RE3zZ2x4tA1CTv9qtyntetox0_-a66sNRUtlmT487HPYXoj8T3oe1td75ntxu7izT61yFbzmfL6Wuy-CjeppNFYrXExGZOAYFGNApXkJuNtaQIMMvJSEsgUK1yAWqtZA5CCefWSJkBJQFXMkuH7PEae5lf7oOvbTiXfzeUlxt64ulK9M2-DxS7ctseQj8tllKgNBqVwfQX4Kxezw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2182958498</pqid></control><display><type>article</type><title>A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property</title><source>Freely Accessible Journals</source><source>arXiv.org</source><creator>Li, Maojun ; Xu, Liwei ; Cheng, Yongping</creator><creatorcontrib>Li, Maojun ; Xu, Liwei ; Cheng, Yongping</creatorcontrib><description>In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1902.05688</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Computer simulation ; Elliptic functions ; Finite element method ; Galerkin method ; Mathematics - Numerical Analysis ; Model accuracy ; Riemann solver ; Shallow water ; Solvers ; Two dimensional models ; Water waves</subject><ispartof>arXiv.org, 2019-02</ispartof><rights>2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27924</link.rule.ids><backlink>$$Uhttps://doi.org/10.1016/j.jcp.2019.108953$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1902.05688$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Li, Maojun</creatorcontrib><creatorcontrib>Xu, Liwei</creatorcontrib><creatorcontrib>Cheng, Yongping</creatorcontrib><title>A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property</title><title>arXiv.org</title><description>In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests.</description><subject>Computer simulation</subject><subject>Elliptic functions</subject><subject>Finite element method</subject><subject>Galerkin method</subject><subject>Mathematics - Numerical Analysis</subject><subject>Model accuracy</subject><subject>Riemann solver</subject><subject>Shallow water</subject><subject>Solvers</subject><subject>Two dimensional models</subject><subject>Water waves</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotkEFPAjEUhBsTEwnyAzzZxPPia7fdfT0ShNWE6IX7WujDLWF3sV1A_r0reJo5fJnMDGMPAsYKtYZnG378cSwMyDHoDPGGDWSaigSVlHdsFOMWAGSWS63TAfuc8OlLkcxnvKauah3ftIF3FfHu1CbO19RE3zZ2x4tA1CTv9qtyntetox0_-a66sNRUtlmT487HPYXoj8T3oe1td75ntxu7izT61yFbzmfL6Wuy-CjeppNFYrXExGZOAYFGNApXkJuNtaQIMMvJSEsgUK1yAWqtZA5CCefWSJkBJQFXMkuH7PEae5lf7oOvbTiXfzeUlxt64ulK9M2-DxS7ctseQj8tllKgNBqVwfQX4Kxezw</recordid><startdate>20190215</startdate><enddate>20190215</enddate><creator>Li, Maojun</creator><creator>Xu, Liwei</creator><creator>Cheng, Yongping</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190215</creationdate><title>A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property</title><author>Li, Maojun ; Xu, Liwei ; Cheng, Yongping</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a528-a6d40e0588948b079faae4e0867e92ae0184b7104c4270141ddc8e6904208b263</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computer simulation</topic><topic>Elliptic functions</topic><topic>Finite element method</topic><topic>Galerkin method</topic><topic>Mathematics - Numerical Analysis</topic><topic>Model accuracy</topic><topic>Riemann solver</topic><topic>Shallow water</topic><topic>Solvers</topic><topic>Two dimensional models</topic><topic>Water waves</topic><toplevel>online_resources</toplevel><creatorcontrib>Li, Maojun</creatorcontrib><creatorcontrib>Xu, Liwei</creatorcontrib><creatorcontrib>Cheng, Yongping</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Maojun</au><au>Xu, Liwei</au><au>Cheng, Yongping</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property</atitle><jtitle>arXiv.org</jtitle><date>2019-02-15</date><risdate>2019</risdate><eissn>2331-8422</eissn><abstract>In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudo-conservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method which possesses an important feature of needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1902.05688</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2019-02
issn 2331-8422
language eng
recordid cdi_arxiv_primary_1902_05688
source Freely Accessible Journals; arXiv.org
subjects Computer simulation
Elliptic functions
Finite element method
Galerkin method
Mathematics - Numerical Analysis
Model accuracy
Riemann solver
Shallow water
Solvers
Two dimensional models
Water waves
title A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-11T18%3A53%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20CDG-FE%20method%20for%20the%20two-dimensional%20Green-Naghdi%20model%20with%20the%20enhanced%20dispersive%20property&rft.jtitle=arXiv.org&rft.au=Li,%20Maojun&rft.date=2019-02-15&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1902.05688&rft_dat=%3Cproquest_arxiv%3E2182958498%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2182958498&rft_id=info:pmid/&rfr_iscdi=true