SIMPLE algorithm - Revision history

CapitalSasha: better link

2024-06-07T21:20:27Z

better link

← Previous revision		Revision as of 21:20, 7 June 2024
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London~~\|Imperial College~~]]~~, London~~ in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London]] in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>

LucasBrown: Importing Wikidata short description: "Computational fluid dynamics algorithm"

2024-05-09T00:18:41Z

Importing Wikidata short description: "Computational fluid dynamics algorithm"

← Previous revision		Revision as of 00:18, 9 May 2024
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			{{Short description\|Computational fluid dynamics algorithm}}
	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

Citation bot: Add: isbn. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | #UCB_webform 1048/3485

2022-10-23T06:14:10Z

Add: isbn. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | #UCB_webform 1048/3485

← Previous revision		Revision as of 06:14, 23 October 2022
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	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>
	A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 }}</ref>		A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 \|isbn=9781560320463 }}</ref>

	== Algorithm ==		== Algorithm ==

111.68.97.205: /* Algorithm */

2022-01-08T15:22:27Z

Algorithm

← Previous revision		Revision as of 15:22, 8 January 2022
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	# Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>		# Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>
	# Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.		# Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.
	# Update density due to pressure changes.f		# Update density due to pressure changes.

	== See also ==		== See also ==

111.68.97.205: /* Algorithm */

2022-01-08T15:19:21Z

Algorithm

← Previous revision		Revision as of 15:19, 8 January 2022
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	# Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>		# Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>
	# Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.		# Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.
	# Update density due to pressure changes.		# Update density due to pressure changes.f

	== See also ==		== See also ==

72.12.202.171: removed dead ref/link

2021-05-09T01:29:59Z

removed dead ref/link

← Previous revision		Revision as of 01:29, 9 May 2021
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.~~<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref>~~<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>

Monkbot: Task 18 (cosmetic): eval 5 templates: del empty params (2×); hyphenate params (1×);

2020-12-30T23:24:42Z

Task 18 (cosmetic): eval 5 templates: del empty params (2×); hyphenate params (1×);

← Previous revision		Revision as of 23:24, 30 December 2020
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|~~accessdate~~=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>
	A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.~~\| author-link =~~ \|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 ~~\|isbn=~~}}</ref>		A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 }}</ref>

	== Algorithm ==		== Algorithm ==

Tom.Reding: Enum 1 author/editor WL; WP:GenFixes on

2020-12-15T16:53:31Z

Enum 1 author/editor WL; WP:GenFixes on

← Previous revision		Revision as of 16:53, 15 December 2020
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	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>
	A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\| author-link = \|author2 = ~~[[Dale~~ A. ~~Anderson~~\|~~Anderson,~~ D. A.]] \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 \|isbn=}}</ref>		A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\| author-link = \|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 \|isbn=}}</ref>

	== Algorithm ==		== Algorithm ==
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	==References==		==References==
	{{~~reflist~~}}		{{Reflist}}

	[[Category:Computational fluid dynamics]]		[[Category:Computational fluid dynamics]]

Frap at 11:14, 10 November 2020

2020-11-10T11:14:16Z

Tom.Reding: MOS:SEEALSO: "#" →‎ "*"; WP:GenFixes on

2020-11-09T16:29:34Z

MOS:SEEALSO: "#" →‎ "*"; WP:GenFixes on

← Previous revision		Revision as of 16:29, 9 November 2020
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	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|accessdate=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|accessdate=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| ~~authorlink~~ = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| ~~authorlink~~ = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>
	A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\| ~~authorlink~~ = \|author2 = [[Dale A. Anderson\|Anderson, D. A.]] \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 \|isbn=}}</ref>		A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\| author-link = \|author2 = [[Dale A. Anderson\|Anderson, D. A.]] \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 \|isbn=}}</ref>

	== Algorithm ==		== Algorithm ==
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	== See also ==		== See also ==

	# [[PISO algorithm]]		* [[PISO algorithm]]
	# [[SIMPLEC algorithm]]		* [[SIMPLEC algorithm]]

	==References==		==References==

← Previous revision		Revision as of 21:20, 7 June 2024
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London~~\|Imperial College~~]]~~, London~~ in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London]] in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>

← Previous revision		Revision as of 01:29, 9 May 2021
Line 1:		Line 1:
	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.~~<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref>~~<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>

← Previous revision		Revision as of 23:24, 30 December 2020
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|~~accessdate~~=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|access-date=2016-03-16}}</ref>

	Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>		Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail.<ref>{{cite book \|last=Patankar \|first=S. V. \| author-link = Suhas Patankar \|title=Numerical Heat Transfer and Fluid Flow \|publisher=[[Taylor & Francis]] \|year=1980 \|isbn=978-0-89116-522-4}}</ref><ref>{{cite book \|last=Ferziger \|first=J. H. \| author-link = J. H. Ferziger \|author2=Peric, M. \|title=Computational Methods for Fluid Dynamics\|publisher=[[Springer-Verlag]] \|year=2001 \|isbn= 978-3-540-42074-3}}</ref>
	A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.~~\| author-link =~~ \|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 ~~\|isbn=~~}}</ref>		A modified variant is the ''SIMPLER'' algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.<ref>{{cite book \|last=Tannehill\|first=J. C.\|author2 = Anderson, D. A. \|author2-link = Dale A. Anderson \|author3=Pletcher, R. H. \|title=Computational Fluid Mechanics and Heat Transfer \|url=https://archive.org/details/computationalflu0000tann\|url-access=registration\|publisher=[[Taylor & Francis]] \|year=1997 }}</ref>

	== Algorithm ==		== Algorithm ==

← Previous revision		Revision as of 11:14, 10 November 2020
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	In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[~~Navier-Stokes~~ equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.		In [[computational fluid dynamics]] (CFD), the '''SIMPLE algorithm''' is a widely used [[numerical algorithm\|numerical procedure]] to solve the [[Navier–Stokes equation]]s. ''SIMPLE'' is an acronym for Semi-Implicit Method for Pressure Linked Equations.

	The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|accessdate=2016-03-16}}</ref>		The SIMPLE algorithm was developed by Prof. [[Brian Spalding]] and his student [[Suhas Patankar]] at [[Imperial College London\|Imperial College]], London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.<ref>{{cite document\|citeseerx=10.1.1.734.2028\|title=SIMPLE solver for driven cavity flow problem}}</ref><ref>{{cite conference \|last1=Mangani \|first1=L. \|last2=Bianchini \|first2=C. \|conference=[[Proceedings of the OpenFOAM International Conference 2007]] \|year=2007 \|url=https://flore.unifi.it/retrieve/handle/2158/418277/15222/OFIC-07.pdf \|title=Heat transfer applications in turbomachinery \|accessdate=2016-03-16}}</ref>
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	The algorithm is [[iterative]]. The basic steps in the solution update are as follows:		The algorithm is [[iterative]]. The basic steps in the solution update are as follows:

	#Set the boundary conditions.		# Set the boundary conditions.
	#Compute the gradients of velocity and pressure.		# Compute the gradients of velocity and pressure.
	#Solve the discretized momentum equation to compute the intermediate velocity field.		# Solve the discretized momentum equation to compute the intermediate velocity field.
	#Compute the uncorrected mass fluxes at faces.		# Compute the uncorrected mass fluxes at faces.
	#Solve the pressure correction equation to produce cell values of the pressure correction.		# Solve the pressure correction equation to produce cell values of the pressure correction.
	#Update the pressure field: <math> p^{k + 1} = p^k + \text{urf} \cdot p^{'} </math> where urf is the under-relaxation factor for pressure.		# Update the pressure field: <math> p^{k + 1} = p^k + \text{urf} \cdot p^{'} </math> where urf is the under-relaxation factor for pressure.
	#Update the boundary pressure corrections <math> p_b^{'} </math>.		# Update the boundary pressure corrections <math> p_b^{'} </math>.
	#Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>		# Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^{*} + \dot m_f^{'} </math>
	#Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.		# Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^{*} - \frac{{\text{Vol} \ \nabla p^{'} }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^{'} } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.
	#Update density due to pressure changes.		# Update density due to pressure changes.

	== See also ==		== See also ==