PISO algorithm - Revision history

BD2412: clean up spacing around commas and other punctuation fixes, replaced: ,M → , M, ,u → , u (8), ,v → , v (8), ; → ; (4)

2024-04-23T23:41:17Z

clean up spacing around commas and other punctuation fixes, replaced: ,M → , M, ,u → , u (8), ,v → , v (8), ; → ; (4)

← Previous revision		Revision as of 23:41, 23 April 2024
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	# http://openfoamwiki.net/index.php/OpenFOAM_guide/The_PISO_algorithm_in_OpenFOAM		# http://openfoamwiki.net/index.php/OpenFOAM_guide/The_PISO_algorithm_in_OpenFOAM
	# Computational fluid dynamics by T. J. Chung, University of Alabama in Huntsville {{ISBN\|0 521 59416 2}}		# Computational fluid dynamics by T. J. Chung, University of Alabama in Huntsville {{ISBN\|0 521 59416 2}}
	# Computational method for fluid dynamics by Joel H.Ferziger,Milovan Peric {{ISBN\|3-540-42074-6}}		# Computational method for fluid dynamics by Joel H.Ferziger, Milovan Peric {{ISBN\|3-540-42074-6}}
	# Solution of the implicitly discretized fluid flow equations by operator-splitting, ''Journal of Computational Physics'' 62 by R. Issa		# Solution of the implicitly discretized fluid flow equations by operator-splitting, ''Journal of Computational Physics'' 62 by R. Issa

Archermarx: /* Algorithm steps */

2023-10-20T00:15:41Z

Algorithm steps

← Previous revision		Revision as of 00:15, 20 October 2023
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	#Increase the time step and repeat from 1.		#Increase the time step and repeat from 1.

	~~As already seen{{where?\|date=June 2019}} for the SIMPLE algorithm, the steps~~ 4 and 5 can be repeated for a prescribed number of times to correct for non-orthogonality.		Steps 4 and 5 can be repeated for a prescribed number of times to correct for non-orthogonality.

	'''Predictor step'''		'''Predictor step'''

165.194.19.70: /* Advantages and disadvantages */

2022-06-19T11:52:54Z

Advantages and disadvantages

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	# For laminar backward facing step PISO is faster than SIMPLE but it is slower concerning flow through heated fin.		# For laminar backward facing step PISO is faster than SIMPLE but it is slower concerning flow through heated fin.
	# If momentum and scalar equation have weak or no coupling then PISO is better than SIMPLEC.		# If momentum and scalar equation have weak or no coupling then PISO is better than SIMPLEC.
			# PISO is most time effective method

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

Frap at 11:14, 4 June 2020

2020-06-04T11:14:00Z

@@ Line 1: / Line 1: @@
 PISO algorithm ('''Pressure-Implicit with''' [[operator splitting|'''Splitting of Operators''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.
@@ Line 60: / Line 59: @@
 ==References==
-. An Introduction to Computational Fluid Dynamics The Finite Volume Method, 2/e
+# An Introduction to Computational Fluid Dynamics The Finite Volume Method, 2/e By Versteeg  {{ISBN|978-0131274983}}
-. Computational Fluid Dynamics for Engineers By Bengt Andersson
+# Computational Fluid Dynamics in Fire Engineering: Theory, Modelling and Practice by Guan Heng Yeoh, Kwok Kit Yuen {{ISBN|978-0750685894}}
 [[Category:Computational fluid dynamics]]

Ira Leviton: Fixed typos found with Wikipedia:Typo_Team/moss.

2019-06-29T19:43:40Z

Fixed typos found with Wikipedia:Typo_Team/moss.

← Previous revision		Revision as of 19:43, 29 June 2019
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	==Introduction==		==Introduction==
	PISO algorithm ('''Pressure-Implicit with''' [[operator splitting\|'''Splitting of Operators''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] ~~(CFD)~~ to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.		PISO algorithm ('''Pressure-Implicit with''' [[operator splitting\|'''Splitting of Operators''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.

	PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.		PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.

	==Algorithm ~~Steps~~==		==Algorithm steps==
	[[File:Flow chart of PISO algorithm.png\|thumb\|407x407px\|Flow chart of PISO algorithm\|center]]		[[File:Flow chart of PISO algorithm.png\|thumb\|407x407px\|Flow chart of PISO algorithm\|center]]

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	#Repeat from 3 for the prescribed number of times.		#Repeat from 3 for the prescribed number of times.
	#Increase the time step and repeat from 1.		#Increase the time step and repeat from 1.

	As already seen for the SIMPLE algorithm, the steps 4 and 5 can be repeated for a prescribed number of times to correct for non-orthogonality.		As already seen{{where?\|date=June 2019}} for the SIMPLE algorithm, the steps 4 and 5 can be repeated for a prescribed number of times to correct for non-orthogonality.
	<br />

	'''Predictor step'''~~<br />~~		'''Predictor step'''
⚫	Guess the pressure field <math>p^</math> and get velocity field components <math>u^</math> and <math>v^*</math> using ~~Discretized~~ momentum equation.The initial guess for the pressure may or may not be correct.<br />

		⚫	Guess the pressure field <math>p^</math> and get velocity field components <math>u^</math> and <math>v^*</math> using discretized momentum equation. The initial guess for the pressure may or may not be correct.<br />
	'''Corrector step 1'''<br />Velocity component obtained from predictor step may not satisfy the continuity equation, so we define correction factors p',v',u' for the pressure field and velocity field. Solve the momentum equation by inserting correct pressure field <math>p^{}</math> and get the corresponding correct velocity components <math>u^{}</math> and <math>v^{**}</math>.		'''Corrector step 1'''<br />Velocity component obtained from predictor step may not satisfy the continuity equation, so we define correction factors p',v',u' for the pressure field and velocity field. Solve the momentum equation by inserting correct pressure field <math>p^{}</math> and get the corresponding correct velocity components <math>u^{}</math> and <math>v^{**}</math>.

	<br />
	<math>p'=p^{*}-p^</math>		<math>p'=p^{*}-p^</math>

	<br />
	<math>v'=v^{*}-v^</math><br />		<math>v'=v^{*}-v^</math><br />
	<math>u'=u^{*}-u^</math><br />		<math>u'=u^{*}-u^</math><br />
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	<math>p^,u^,v^*</math> :guessed pressure field and velocity component<br />		<math>p^,u^,v^*</math> :guessed pressure field and velocity component<br />
	We define <math>p',u',v'</math> as above.		We define <math>p',u',v'</math> as above.
	By putting the correct pressure field <math>p^{}</math> into the discretized momentum equation we get the correct velocity components <math>v^{}</math> and <math>u^{**}</math>. Once the pressure correction <math>p'</math> is known we can find the correction components for the velocity: <math>u'</math> and <math>v'</math> .		By putting the correct pressure field <math>p^{}</math> into the discretized momentum equation we get the correct velocity components <math>v^{}</math> and <math>u^{**}</math>. Once the pressure correction <math>p'</math> is known we can find the correction components for the velocity: <math>u'</math> and <math>v'</math>.

	'''Corrector step 2'''		'''Corrector step 2'''
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	where : <math>p^{*},v^{},u^{**}</math> are the correct pressure field and the correct velocity components, respectively<br />		where : <math>p^{*},v^{},u^{**}</math> are the correct pressure field and the correct velocity components, respectively<br />
	and <math>p'',v'',u''</math> are second corrections to the pressure and velocity field.<br />		and <math>p'',v'',u''</math> are second corrections to the pressure and velocity field.<br />
	Set <math>p=p^{*}, v=v^{}, u=u^{**}</math>		Set <math>p=p^{*}, v=v^{}, u=u^{**}</math>
	where ; <math>p,v,u</math> are correct pressure and velocity field		where; <math>p,v,u</math> are correct pressure and velocity field

	==Advantages and disadvantages==		==Advantages and disadvantages==

134.169.84.55: /* Introduction */

2018-01-16T15:56:56Z

Introduction

← Previous revision		Revision as of 15:56, 16 January 2018
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	==Introduction==		==Introduction==
	PISO algorithm ('''Pressure Implicit with''' [[operator splitting\|'''Splitting of ~~Operator~~''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] (CFD) to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.		PISO algorithm ('''Pressure-Implicit with''' [[operator splitting\|'''Splitting of Operators''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] (CFD) to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.

	PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.		PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.

PrimeBOT: Replace magic links with templates per local RfC - BRFA

2017-06-25T22:41:15Z

Replace magic links with templates per local RfC - BRFA

← Previous revision		Revision as of 22:41, 25 June 2017
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	==References==		==References==
	1. An Introduction to Computational Fluid Dynamics The Finite Volume Method, 2/e		1. An Introduction to Computational Fluid Dynamics The Finite Volume Method, 2/e
	By Versteeg ISBN 978-0131274983 <br />		By Versteeg {{ISBN\|978-0131274983}} <br />
	2. Computational Fluid Dynamics for Engineers By Bengt Andersson		2. Computational Fluid Dynamics for Engineers By Bengt Andersson
	Ronnie Andersson		Ronnie Andersson
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	Rahman Sudiyo		Rahman Sudiyo
	Berend van Wachem		Berend van Wachem
	ISBN 978-1-107-01895-2 <br />		{{ISBN\|978-1-107-01895-2}} <br />
	3. Computational Fluid Dynamics in Fire Engineering: Theory, Modelling and Practice		3. Computational Fluid Dynamics in Fire Engineering: Theory, Modelling and Practice
	By Guan Heng Yeoh, Kwok Kit Yuen ISBN 978-0750685894<br />		By Guan Heng Yeoh, Kwok Kit Yuen {{ISBN\|978-0750685894}}<br />
	4.http://openfoamwiki.net/index.php/OpenFOAM_guide/The_PISO_algorithm_in_OpenFOAM<br />		4.http://openfoamwiki.net/index.php/OpenFOAM_guide/The_PISO_algorithm_in_OpenFOAM<br />
	5. Computational fluid dynamics BY T. J. CHUNG University of Alabama in Huntsville ISBN 0 521 59416 2<br />		5. Computational fluid dynamics BY T. J. CHUNG University of Alabama in Huntsville {{ISBN\|0 521 59416 2}}<br />
	6. Computational method for fluid dynamics by Joel H.Ferziger,Milovan Peric ISBN 3-540-42074-6<br />		6. Computational method for fluid dynamics by Joel H.Ferziger,Milovan Peric {{ISBN\|3-540-42074-6}}<br />
	7. Solution of the implicitly discretized fluid flow equations by operator-splitting, Journal of Computational Physics 62 by R. Issa		7. Solution of the implicitly discretized fluid flow equations by operator-splitting, Journal of Computational Physics 62 by R. Issa

Anita5192: /* Introduction */ Moved abbreviation after full name

2017-04-12T21:07:14Z

Introduction: Moved abbreviation after full name

← Previous revision		Revision as of 21:07, 12 April 2017
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	==Introduction==		==Introduction==
	PISO algorithm ('''Pressure Implicit with''' [[operator splitting\|'''Splitting of Operator''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in ~~CFD~~ [[computational fluid dynamics]] to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.		PISO algorithm ('''Pressure Implicit with''' [[operator splitting\|'''Splitting of Operator''']]) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the [[SIMPLE algorithm]] used in [[computational fluid dynamics]] (CFD) to solve the Navier-Stokes equations. PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressible flow, but it has been adapted successfully to steady-state problems.

	PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.		PISO involves one predictor step and two corrector steps and is designed to satisfy mass conservation using predictor-corrector steps.

210.107.186.171: /* Algorithm Steps */

2017-04-12T08:00:38Z

Algorithm Steps

← Previous revision		Revision as of 08:00, 12 April 2017
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	==Algorithm Steps==		==Algorithm Steps==
	[[File:Flow chart of PISO algorithm.png\|thumb\|~~600x489px\|right~~\|Flow chart of PISO algorithm]]		[[File:Flow chart of PISO algorithm.png\|thumb\|407x407px\|Flow chart of PISO algorithm\|center]]

	The algorithm can be summed up as follows:		The algorithm can be summed up as follows:

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2017-04-12T07:58:23Z

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	==Algorithm Steps==		==Algorithm Steps==
	[[File:Flow chart of PISO algorithm.png\|thumb\|600x489px\|right\|Flow chart of PISO algorithm]]		[[File:Flow chart of PISO algorithm.png\|thumb\|600x489px\|right\|Flow chart of PISO algorithm]]

	The algorithm can be summed up as follows:		The algorithm can be summed up as follows:
	#Set the boundary conditions.		#Set the boundary conditions.