SIMPLEC algorithm - Revision history

144.32.240.92: /* Algorithm */

2024-04-09T09:06:47Z

Algorithm

← Previous revision		Revision as of 09:06, 9 April 2024
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	== Algorithm ==		== Algorithm ==
	The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. '''p, u, v*''' are guessed Pressure, X-direction velocity and Y-direction velocity respectively, '''p', u', v'''' are the correction terms respectively and '''p, u, v''' are the correct fields respectively; '''Φ''' is the property for which we are solving and '''d''' terms are involved with the under relaxation factor. So, steps are as follows:		The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. '''p, u, v*''' are guessed Pressure, X-direction velocity and Y-direction velocity respectively, '''p', u', v'''' are the correction terms respectively and '''p, u, v''' are the correct fields respectively; '''Φ''' is the property for which we are solving and '''d''' terms are involved with the under relaxation factor. So, steps are as follows:

	# Specify the boundary conditions and guess the initial values.		1. Specify the boundary conditions and guess the initial values.
⚫	# Determine the velocity and pressure gradients.

⚫	# Calculate the pseudo velocities.
		⚫	2. Determine the velocity and pressure gradients.

		⚫	3. Calculate the pseudo velocities.

	:::<math>\hat{u}_{i,J}=\frac{\sum a_{nb}u^*_{nb}+b_{i,J}}{a_{i,J}}</math>		:::<math>\hat{u}_{i,J}=\frac{\sum a_{nb}u^*_{nb}+b_{i,J}}{a_{i,J}}</math>
	:::<math>\hat{v}_{I,j}=\frac{\sum a_{nb}v^*_{nb}+b_{I,j}}{a_{I,j}}</math>		:::<math>\hat{v}_{I,j}=\frac{\sum a_{nb}v^*_{nb}+b_{I,j}}{a_{I,j}}</math>

	# Solve for the pressure equation and get the '''p'''.		4. Solve for the pressure equation and get the '''p'''.

	:::<math>a_{I,J}p_{I,J} =		:::<math>a_{I,J}p_{I,J} =
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	+ a_{I,J-1}p_{I,J-1} + a_{I,J+1}p_{I,J+1} + b_{I,J}</math>		+ a_{I,J-1}p_{I,J-1} + a_{I,J+1}p_{I,J+1} + b_{I,J}</math>

	# Set '''p*'''='''p'''.		5. Set '''p*'''='''p'''.

	# Using '''p''' solve the discretized momentum equation and get '''u''' and '''v*'''.		6. Using '''p''' solve the discretized momentum equation and get '''u''' and '''v*'''.

	:::<math> a_{i,J} u^_{i,J}=\sum a_{nb}u^_{nb} +		:::<math> a_{i,J} u^_{i,J}=\sum a_{nb}u^_{nb} +
	(p^_{I-1,J} - p^_{I,J})A_{i,J} + b_{i,J}</math>		(p^_{I-1,J} - p^_{I,J})A_{i,J} + b_{i,J}</math>
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	(p^_{I,J-1} - p^_{I,J})A_{I,j} + b_{I,j}</math>		(p^_{I,J-1} - p^_{I,J})A_{I,j} + b_{I,j}</math>

	# Solve the pressure correction equation.		7. Solve the pressure correction equation.

	:::<math>a_{I,J}p'_{I,J} =		:::<math>a_{I,J}p'_{I,J} =
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	+ a_{I,J-1}p'_{I,J-1} + a_{I,J+1}p'_{I,J+1} + b'_{I,J}</math>		+ a_{I,J-1}p'_{I,J-1} + a_{I,J+1}p'_{I,J+1} + b'_{I,J}</math>

	# Get the pressure correction term and evaluate the corrected velocities and get '''p, u, v, Φ*'''.		8. Get the pressure correction term and evaluate the corrected velocities and get '''p, u, v, Φ*'''.

	:::<math> u_{i,J}=u^*_{i,J} +		:::<math> u_{i,J}=u^*_{i,J} +
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	d_{I,j}(p'_{I,J-1} - p'_{I,J}) </math>		d_{I,j}(p'_{I,J-1} - p'_{I,J}) </math>

	# Solve all other discretized transport equations.		9. Solve all other discretized transport equations.

	:::<math>a_{I,J}\phi_{I,J} =		:::<math>a_{I,J}\phi_{I,J} =
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	+ a_{I,J-1}\phi_{I,J-1} + a_{I,J+1}\phi_{I,J+1} + b^{\phi}_{I,J}</math>		+ a_{I,J-1}\phi_{I,J-1} + a_{I,J+1}\phi_{I,J+1} + b^{\phi}_{I,J}</math>

	# If Φ shows convergence, then STOP and if not, then set '''p=p, u=u, v=v, Φ=Φ''' and start the iteration again.<br /><ref>{{cite book\|last1=Versteeg\|first1=H.K.\|last2=Malalasekera\|first2=W.\|title=An introduction to Computational Fluid Dynamics- The finite volume method\|publisher=Longman Group Ltd.\|pages=149–151\|edition=1st edition, 1995}}</ref><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>		10. If Φ shows convergence, then STOP and if not, then set '''p=p, u=u, v=v, Φ=Φ''' and start the iteration again.<br /><ref>{{cite book\|last1=Versteeg\|first1=H.K.\|last2=Malalasekera\|first2=W.\|title=An introduction to Computational Fluid Dynamics- The finite volume method\|publisher=Longman Group Ltd.\|pages=149–151\|edition=1st edition, 1995}}</ref><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>
	[[File:Pseudo velocity equations in x and y dir..JPG\|thumb\|Pseudo velocity equations in x and y dir.]]		[[File:Pseudo velocity equations in x and y dir..JPG\|thumb\|Pseudo velocity equations in x and y dir.]]
	[[File:Pressure equation.JPG\|thumb\|Pressure equation]]		[[File:Pressure equation.JPG\|thumb\|Pressure equation]]

PianoDan: Rewrite for clarity

2022-12-21T18:03:00Z

Rewrite for clarity

← Previous revision		Revision as of 18:03, 21 December 2022
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	{{Short description\|Numerical approximate solution to the Navier–Stokes equations}}		{{Short description\|Numerical approximate solution to the Navier–Stokes equations}}
	The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in the field of [[computational fluid dynamics]] to solve the ~~famous~~ [[Navier–Stokes equations]].		The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in the field of [[computational fluid dynamics]] to solve the [[Navier–Stokes equations]].

	This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps ~~like~~ the [[SIMPLE algorithm]] with ~~a little~~ variation that the momentum equations are manipulated ~~which~~ ~~allows~~ SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. ~~Basically,~~ it ~~tries~~ to ~~prevent~~ the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />		This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps as the [[SIMPLE algorithm]], with the variation that the momentum equations are manipulated, allowing the SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. This modification attempts to minimize the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />

	== Algorithm ==		== Algorithm ==

The Anome: copyedit, link

2022-12-20T18:44:33Z

copyedit, link

← Previous revision		Revision as of 18:44, 20 December 2022
Line 1:		Line 1:
	{{Short description\|Numerical approximate solution to the Navier–Stokes equations}}		{{Short description\|Numerical approximate solution to the Navier–Stokes equations}}
	The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in ~~Computational~~ ~~Fluid~~ ~~Dynamics~~ to solve the ~~very~~ famous [[Navier–Stokes equations]].		The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in the field of [[computational fluid dynamics]] to solve the famous [[Navier–Stokes equations]].

	This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />		This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />

The Anome: Adding short description: "Numerical approximate solution to the Navier–Stokes equations"

2022-12-20T18:39:08Z

Adding short description: "Numerical approximate solution to the Navier–Stokes equations"

← Previous revision		Revision as of 18:39, 20 December 2022
Line 1:		Line 1:
			{{Short description\|Numerical approximate solution to the Navier–Stokes equations}}
	The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[Navier–Stokes equations]].		The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[Navier–Stokes equations]].

Frap at 13:05, 30 March 2020

2020-03-30T13:05:57Z

← Previous revision		Revision as of 13:05, 30 March 2020
Line 1:		Line 1:
	The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[~~Navier-Stokes~~ equations]].~~<br />~~		The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[Navier–Stokes equations]].

	This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />		This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />

	== Algorithm ==		== Algorithm ==
	The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature.'''p, u, v*''' are guessed Pressure, X-direction velocity and Y-direction velocity respectively, '''p', u', v'''' are the correction terms respectively and '''p, u, v''' are the correct fields respectively; '''Φ''' is the property for which we are solving and '''d''' terms are involved with the under relaxation factor. So, steps are as follows:		The steps involved are same as the SIMPLE algorithm and the algorithm is iterative in nature. '''p, u, v*''' are guessed Pressure, X-direction velocity and Y-direction velocity respectively, '''p', u', v'''' are the correction terms respectively and '''p, u, v''' are the correct fields respectively; '''Φ''' is the property for which we are solving and '''d''' terms are involved with the under relaxation factor. So, steps are as follows:
	# Specify the boundary conditions and guess the initial values.		# Specify the boundary conditions and guess the initial values.
	# Determine the velocity and pressure gradients.		# Determine the velocity and pressure gradients.
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	* [[SIMPLE algorithm]]		* [[SIMPLE algorithm]]
	* [[SIMPLER algorithm]]		* [[SIMPLER algorithm]]
	* [[~~Navier-Stokes~~ equations]]		* [[Navier–Stokes equations]]

	== References ==		== References ==

GoodDay: per WP:BOLDTITLE

2020-02-15T18:09:45Z

per WP:BOLDTITLE

← Previous revision		Revision as of 18:09, 15 February 2020
Line 1:		Line 1:
	The SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[Navier-Stokes equations]].<br />		The '''SIMPLEC''' (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm; a modified form of [[SIMPLE algorithm]]; is a commonly used numerical procedure in Computational Fluid Dynamics to solve the very famous [[Navier-Stokes equations]].<br />
	This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />		This algorithm was developed by Van Doormal and Raithby in 1984. The algorithm follows the same steps like the [[SIMPLE algorithm]] with a little variation that the momentum equations are manipulated which allows SIMPLEC velocity correction equations to omit terms that are less significant than those omitted in SIMPLE. Basically, it tries to prevent the effects of dropping velocity neighbor correction terms.<ref>{{cite web\|title=Variants of SIMPLE algorithm\|url=https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf\|website=engineering.purdue.edu\|accessdate=11 November 2014}}</ref><br />

200.104.41.177: /* Algorithm */

2016-12-01T23:52:59Z

Algorithm

200.104.41.177: /* Algorithm */

2016-12-01T23:52:13Z

Algorithm

← Previous revision		Revision as of 23:52, 1 December 2016
Line 8:		Line 8:
	# Calculate the pseudo velocities.		# Calculate the pseudo velocities.

	:<math>\hat{u}_{i,J}=\frac{\sum a_{nb}u^*_{nb}+b_{i,J}}{a_{i,J}}</math>		::<math>\hat{u}_{i,J}=\frac{\sum a_{nb}u^*_{nb}+b_{i,J}}{a_{i,J}}</math>
	:<math>\hat{v}_{I,j}=\frac{\sum a_{nb}v^*_{nb}+b_{I,j}}{a_{I,j}}</math>		:<math>\hat{v}_{I,j}=\frac{\sum a_{nb}v^*_{nb}+b_{I,j}}{a_{I,j}}</math>

200.104.41.177: /* Algorithm */

2016-12-01T23:51:53Z

Algorithm

@@ Line 12: / Line 12: @@
 # Solve for the pressure equation and get the '''p'''.
 # Set '''p*'''='''p'''.
 # Using '''p*''' solve the discretized momentum equation and get '''u*''' and '''v*'''.
 # Solve the pressure correction equation.
 # Get the pressure correction term and evaluate the corrected velocities and get '''p, u, v, Φ*'''.
 # Solve all other discretized transport equations.
 # If Φ shows convergence, then STOP and if not, then set '''p*=p, u*=u, v*=v, Φ*=Φ''' and start the iteration again.<br /><ref>{{cite book|last1=Versteeg|first1=H.K.|last2=Malalasekera|first2=W.|title=An introduction to Computational Fluid Dynamics- The finite volume method|publisher=Longman Group Ltd.|pages=149–151|edition=1st edition, 1995}}</ref><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>
 [[File:Pseudo velocity equations in x and y dir..JPG|thumb|Pseudo velocity equations in x and y dir.]]

200.104.41.177: /* Algorithm */

2016-12-01T23:32:07Z

Algorithm

← Previous revision		Revision as of 23:32, 1 December 2016
Line 7:		Line 7:
	# Determine the velocity and pressure gradients.		# Determine the velocity and pressure gradients.
	# Calculate the pseudo velocities.		# Calculate the pseudo velocities.

			:<math>\hat{u}_{i,J}=\frac{\sum a_{nb}u^*_{nb}+b_{i,J}}{a_{i,J}}</math>
			:<math>\hat{v}_{I,j}=\frac{\sum a_{nb}v^*_{nb}+b_{I,j}}{a_{I,j}}</math>

	# Solve for the pressure equation and get the '''p'''.		# Solve for the pressure equation and get the '''p'''.
	# Set '''p*'''='''p'''.		# Set '''p*'''='''p'''.