A fourth-order compact finite difference method for solving natural convection in rectangular enclosures

A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and tem...

Full description

Saved in:
Bibliographic Details
Main Authors: Leonard, Christopher, Harahap, Caesar Ondolan
Format: Conference Proceeding
Language:English
Subjects:
Advection-diffusion equation
Enclosures
Finite difference method
Free convection
Mathematical analysis
Numerical methods
Poisson equation
Runge-Kutta method
Vorticity
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue 1
container_start_page
container_title
container_volume 2836
creator Leonard, Christopher
Harahap, Caesar Ondolan
description A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and temperature. Then, a different fourth-order compact finite difference method was utilized to solve the Poisson’s equation for the stream function. The system of equations is then time-marched using a fourth-order Runge-Kutta method. The numerical method is then validated by applying it to the natural convection in a square cavity problem. It is shown that good agreement with results of the benchmark solution can be obtained with much fewer grid points.
doi_str_mv 10.1063/5.0188442
format conference_proceeding
fullrecord <record><control><sourceid>proquest_scita</sourceid><recordid>TN_cdi_scitation_primary_10_1063_5_0188442</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3031403572</sourcerecordid><originalsourceid>FETCH-LOGICAL-p1682-96105b90e0ab882c264de35f647290ce0e50cb379841ac3af26a4579136a83cb3</originalsourceid><addsrcrecordid>eNotkE1LAzEQhoMoWKsH_0HAm7B18rnZYyl-QcGLgrclzWbblG2yJtmC_94Ue5qBed6Zd16E7gksCEj2JBZAlOKcXqAZEYJUtSTyEs0AGl5Rzr6v0U1KewDa1LWaod0S92GKeVeF2NmITTiM2mTcO--yxZ3rexutNxYfbN6FrtARpzAcnd9ir_MU9VBE_mhNdsFj53EsrfbbadARF-UQ0hRtukVXvR6SvTvXOfp6ef5cvVXrj9f31XJdjUQqWjWSgNg0YEFvlKKGSt5ZJnrJa9qAsWAFmA2rG8WJNkz3VGou6oYwqRUrkzl6-N87xvAz2ZTbffnPl5MtA0Y4MFHTQj3-U8m4rE_O2zG6g46_LYH2lGQr2nOS7A96JmY7</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype><pqid>3031403572</pqid></control><display><type>conference_proceeding</type><title>A fourth-order compact finite difference method for solving natural convection in rectangular enclosures</title><source>American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list)</source><creator>Leonard, Christopher ; Harahap, Caesar Ondolan</creator><contributor>Indarto ; Saptoadi, Harwin ; Deendarlianto ; Kamal, Samsul ; Ariyadi, Hifni Mukhtar</contributor><creatorcontrib>Leonard, Christopher ; Harahap, Caesar Ondolan ; Indarto ; Saptoadi, Harwin ; Deendarlianto ; Kamal, Samsul ; Ariyadi, Hifni Mukhtar</creatorcontrib><description>A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and temperature. Then, a different fourth-order compact finite difference method was utilized to solve the Poisson’s equation for the stream function. The system of equations is then time-marched using a fourth-order Runge-Kutta method. The numerical method is then validated by applying it to the natural convection in a square cavity problem. It is shown that good agreement with results of the benchmark solution can be obtained with much fewer grid points.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/5.0188442</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Advection-diffusion equation ; Enclosures ; Finite difference method ; Free convection ; Mathematical analysis ; Numerical methods ; Poisson equation ; Runge-Kutta method ; Vorticity</subject><ispartof>AIP conference proceedings, 2024, Vol.2836 (1)</ispartof><rights>Author(s)</rights><rights>2024 Author(s). Published under an exclusive license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><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>309,310,314,776,780,785,786,23909,23910,25118,27901,27902</link.rule.ids></links><search><contributor>Indarto</contributor><contributor>Saptoadi, Harwin</contributor><contributor>Deendarlianto</contributor><contributor>Kamal, Samsul</contributor><contributor>Ariyadi, Hifni Mukhtar</contributor><creatorcontrib>Leonard, Christopher</creatorcontrib><creatorcontrib>Harahap, Caesar Ondolan</creatorcontrib><title>A fourth-order compact finite difference method for solving natural convection in rectangular enclosures</title><title>AIP conference proceedings</title><description>A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and temperature. Then, a different fourth-order compact finite difference method was utilized to solve the Poisson’s equation for the stream function. The system of equations is then time-marched using a fourth-order Runge-Kutta method. The numerical method is then validated by applying it to the natural convection in a square cavity problem. It is shown that good agreement with results of the benchmark solution can be obtained with much fewer grid points.</description><subject>Advection-diffusion equation</subject><subject>Enclosures</subject><subject>Finite difference method</subject><subject>Free convection</subject><subject>Mathematical analysis</subject><subject>Numerical methods</subject><subject>Poisson equation</subject><subject>Runge-Kutta method</subject><subject>Vorticity</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2024</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNotkE1LAzEQhoMoWKsH_0HAm7B18rnZYyl-QcGLgrclzWbblG2yJtmC_94Ue5qBed6Zd16E7gksCEj2JBZAlOKcXqAZEYJUtSTyEs0AGl5Rzr6v0U1KewDa1LWaod0S92GKeVeF2NmITTiM2mTcO--yxZ3rexutNxYfbN6FrtARpzAcnd9ir_MU9VBE_mhNdsFj53EsrfbbadARF-UQ0hRtukVXvR6SvTvXOfp6ef5cvVXrj9f31XJdjUQqWjWSgNg0YEFvlKKGSt5ZJnrJa9qAsWAFmA2rG8WJNkz3VGou6oYwqRUrkzl6-N87xvAz2ZTbffnPl5MtA0Y4MFHTQj3-U8m4rE_O2zG6g46_LYH2lGQr2nOS7A96JmY7</recordid><startdate>20240403</startdate><enddate>20240403</enddate><creator>Leonard, Christopher</creator><creator>Harahap, Caesar Ondolan</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20240403</creationdate><title>A fourth-order compact finite difference method for solving natural convection in rectangular enclosures</title><author>Leonard, Christopher ; Harahap, Caesar Ondolan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1682-96105b90e0ab882c264de35f647290ce0e50cb379841ac3af26a4579136a83cb3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Advection-diffusion equation</topic><topic>Enclosures</topic><topic>Finite difference method</topic><topic>Free convection</topic><topic>Mathematical analysis</topic><topic>Numerical methods</topic><topic>Poisson equation</topic><topic>Runge-Kutta method</topic><topic>Vorticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Leonard, Christopher</creatorcontrib><creatorcontrib>Harahap, Caesar Ondolan</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Leonard, Christopher</au><au>Harahap, Caesar Ondolan</au><au>Indarto</au><au>Saptoadi, Harwin</au><au>Deendarlianto</au><au>Kamal, Samsul</au><au>Ariyadi, Hifni Mukhtar</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>A fourth-order compact finite difference method for solving natural convection in rectangular enclosures</atitle><btitle>AIP conference proceedings</btitle><date>2024-04-03</date><risdate>2024</risdate><volume>2836</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>A new fourth order compact finite difference method for solving transient natural convection in rectangular enclosures is developed. First, finite difference approximations based on Padé schemes are developed to discretize spatial derivatives in the advection-diffusion equations of vorticity and temperature. Then, a different fourth-order compact finite difference method was utilized to solve the Poisson’s equation for the stream function. The system of equations is then time-marched using a fourth-order Runge-Kutta method. The numerical method is then validated by applying it to the natural convection in a square cavity problem. It is shown that good agreement with results of the benchmark solution can be obtained with much fewer grid points.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0188442</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0094-243X
ispartof AIP conference proceedings, 2024, Vol.2836 (1)
issn 0094-243X
1551-7616
language eng
recordid cdi_scitation_primary_10_1063_5_0188442
source American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list)
subjects Advection-diffusion equation
Enclosures
Finite difference method
Free convection
Mathematical analysis
Numerical methods
Poisson equation
Runge-Kutta method
Vorticity
title A fourth-order compact finite difference method for solving natural convection in rectangular enclosures
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-04T09%3A48%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_scita&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=proceeding&rft.atitle=A%20fourth-order%20compact%20finite%20difference%20method%20for%20solving%20natural%20convection%20in%20rectangular%20enclosures&rft.btitle=AIP%20conference%20proceedings&rft.au=Leonard,%20Christopher&rft.date=2024-04-03&rft.volume=2836&rft.issue=1&rft.issn=0094-243X&rft.eissn=1551-7616&rft.coden=APCPCS&rft_id=info:doi/10.1063/5.0188442&rft_dat=%3Cproquest_scita%3E3031403572%3C/proquest_scita%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-p1682-96105b90e0ab882c264de35f647290ce0e50cb379841ac3af26a4579136a83cb3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=3031403572&rft_id=info:pmid/&rfr_iscdi=true