Fipy and Cantera/Diffusion 1D - Revision history

Admin: /* Download The Script */

2017-04-17T07:33:25Z

Download The Script

← Older revision		Revision as of 07:33, 17 April 2017
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	[[Image:OneVarCanteraVariableD.png]]		[[Image:OneVarCanteraVariableD.png]]

	~~=Download The Script=~~

	~~Download the script here: http://charlesmartinreid.com/files/OneVarCanteraVariableD.py~~

	=References=		=References=

Admin at 07:33, 17 April 2017

2017-04-17T07:33:12Z

← Older revision		Revision as of 07:33, 17 April 2017
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	Begin with import statements:		Begin with import statements:

	<~~source lang="python"~~>		<pre>
	from fipy import *		from fipy import *
	from numpy import *		from numpy import *
	import Cantera		import Cantera
	import matplotlib.pylab as plt		import matplotlib.pylab as plt
	</~~source~~>		</pre>

	Next, create a plot, which we'll use to visualize our results:		Next, create a plot, which we'll use to visualize our results:

	<~~source~~>		<pre>
	fig = plt.figure()		fig = plt.figure()
	ax = fig.add_subplot(111)		ax = fig.add_subplot(111)
	ax.set_title('Ar')		ax.set_title('Ar')
	</~~source~~>		</pre>

	Computing the diffusion coefficient using Cantera proceeds as follows:		Computing the diffusion coefficient using Cantera proceeds as follows:
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	We'll define this in a function, which we can then pass when specifying the diffusion coefficient for the Fipy equation. (Note that I'm going to use two global variables here, <code>a</code> and <code>ari</code>, which are defined later in the script. These represent the gas phase object and the argon species index, respectively.)		We'll define this in a function, which we can then pass when specifying the diffusion coefficient for the Fipy equation. (Note that I'm going to use two global variables here, <code>a</code> and <code>ari</code>, which are defined later in the script. These represent the gas phase object and the argon species index, respectively.)

	<~~source~~>		<pre>
	######################################		######################################
	# Diffusion coefficient function		# Diffusion coefficient function
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	return D		return D
	</~~source~~>		</pre>

	We also want to define a single Cantera phase, which we'll use in the <code>get_diffusion_coeff()</code> function:		We also want to define a single Cantera phase, which we'll use in the <code>get_diffusion_coeff()</code> function:

	<~~source~~>		<pre>
	######################################		######################################
	# Gas object		# Gas object
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	ari = a.speciesIndex(arlab)		ari = a.speciesIndex(arlab)
	o2i = a.speciesIndex(o2lab)		o2i = a.speciesIndex(o2lab)
	</~~source~~>		</pre>

	Now we define Fipy equations/grid:		Now we define Fipy equations/grid:

	<~~source~~>		<pre>
	# First, define the mesh		# First, define the mesh
	nx = 100		nx = 100
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	# Now define your sweep variables		# Now define your sweep variables
	arvar = [CellVariable(name=arlab, mesh=mesh, value=arRight, hasOld=1)]		arvar = [CellVariable(name=arlab, mesh=mesh, value=arRight, hasOld=1)]
	</~~source~~>		</pre>

	At this point, we can define the Fipy equation that we're solving, which is, as given above,		At this point, we can define the Fipy equation that we're solving, which is, as given above,
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	and the diffusion coefficient is a function of <math>X_i</math>. This is subject to the boundary conditions set above (1 on the left side of the domain, 0 on the right side of the domain).		and the diffusion coefficient is a function of <math>X_i</math>. This is subject to the boundary conditions set above (1 on the left side of the domain, 0 on the right side of the domain).

	<~~source~~>		<pre>
	# Define the equation being solved		# Define the equation being solved
	eq = TransientTerm() == DiffusionTerm(coeff=get_diffusion_coeff(arvar[0]))		eq = TransientTerm() == DiffusionTerm(coeff=get_diffusion_coeff(arvar[0]))
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	arvar[0].constrain(arLeft, mesh.facesLeft)		arvar[0].constrain(arLeft, mesh.facesLeft)
	arvar[0].constrain(arRight, mesh.facesRight)		arvar[0].constrain(arRight, mesh.facesRight)
	</~~source~~>		</pre>

	Now we timestep through the solutions, and plot the solution every 50 timesteps. At each timestep, we are performing 5 sweeps (that is, we're performing 5 iterations per timestep). Again, our diffusion coefficient is not a strong function of composition, because Ar and O2 are so similar in shape/properties, so even 5 sweeps is probably unnecessary. Again, this is purely for illustrative purposes.		Now we timestep through the solutions, and plot the solution every 50 timesteps. At each timestep, we are performing 5 sweeps (that is, we're performing 5 iterations per timestep). Again, our diffusion coefficient is not a strong function of composition, because Ar and O2 are so similar in shape/properties, so even 5 sweeps is probably unnecessary. Again, this is purely for illustrative purposes.

	<~~source~~>		<pre>
	# Timestep through solutions		# Timestep through solutions
	arvar[0].setValue(arRight)		arvar[0].setValue(arRight)
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	plt.show()		plt.show()
	plt.draw()		plt.draw()
	</~~source~~>		</pre>

	=Result=		=Result=

Admin: /* References */

2017-04-17T07:32:26Z

References

← Older revision		Revision as of 07:32, 17 April 2017
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	Fipy documentation covering 1D diffusion problems: http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html		Fipy documentation covering 1D diffusion problems: http://www.ctcms.nist.gov/fipy/examples/diffusion/generated/examples.diffusion.mesh1D.html

	~~[[Category:Cantera]]~~		{{CanteraFlag}}
	[[Category:Fipy]]		[[Category:Fipy]]

Admin: /* Overview */

2017-04-17T07:31:46Z

Overview

← Older revision		Revision as of 07:31, 17 April 2017
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	=Overview=		=Overview=

	This example illustrates how to solve a simple, time-dependent 1D diffusion problem using [[Fipy]] with diffusion ~~coefficeints~~ computed by [[Cantera]]. This is a very simple problem. The point is not to demonstrate earth-shaking complexity, the point is illustrating how to make these two packages talk to each other.		This example illustrates how to solve a simple, time-dependent 1D diffusion problem using [[Fipy]] with diffusion coefficients computed by [[Cantera]]. This is a very simple problem. The point is not to demonstrate earth-shaking complexity, the point is illustrating how to make these two packages talk to each other.

	The equation being solved is:		The equation being solved is:

Admin: moved Fipy and Cantera/1D Diffusion to Fipy and Cantera/Diffusion 1D

2014-01-16T20:01:27Z

moved Fipy and Cantera/1D Diffusion to Fipy and Cantera/Diffusion 1D

← Older revision	Revision as of 20:01, 16 January 2014
(No difference)

Admin: /* The Script */

2014-01-03T19:21:20Z

The Script

← Older revision		Revision as of 19:21, 3 January 2014
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	ari = a.speciesIndex(arlab)		ari = a.speciesIndex(arlab)
	o2i = a.speciesIndex(o2lab)		o2i = a.speciesIndex(o2lab)
	</~~pre~~>		</source>

	Now we define Fipy equations/grid:		Now we define Fipy equations/grid:

	<~~pre~~>		<source>
	# First, define the mesh		# First, define the mesh
	nx = 100		nx = 100

Admin: /* The Script */

2013-12-20T00:03:13Z

The Script

← Older revision		Revision as of 00:03, 20 December 2013
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	* Return the diffusion CellVariable		* Return the diffusion CellVariable

	We'll define this in a function, which we can then pass when specifying the diffusion coefficient for the Fipy equation.		We'll define this in a function, which we can then pass when specifying the diffusion coefficient for the Fipy equation. (Note that I'm going to use two global variables here, <code>a</code> and <code>ari</code>, which are defined later in the script. These represent the gas phase object and the argon species index, respectively.)

	<source>		<source>

Admin at 00:01, 20 December 2013

2013-12-20T00:01:57Z

← Older revision		Revision as of 00:01, 20 December 2013
Line 1:		Line 1:
	=Overview=		=Overview=

	This example illustrates how to solve a simple, time-dependent 1D diffusion problem using [[Fipy]] with diffusion coefficeints computed by [[Cantera]].		This example illustrates how to solve a simple, time-dependent 1D diffusion problem using [[Fipy]] with diffusion coefficeints computed by [[Cantera]]. This is a very simple problem. The point is not to demonstrate earth-shaking complexity, the point is illustrating how to make these two packages talk to each other.

	The equation being solved is:		The equation being solved is:
Line 23:		Line 23:

	would normally apply, this example illustrates the sweep solution technique (in which the diffusion coefficient is a function of the composition) anyway.		would normally apply, this example illustrates the sweep solution technique (in which the diffusion coefficient is a function of the composition) anyway.

			Note that because this is a binary mixture, we only need to solve for a single component (argon), because:

			<math>
			\sum_i X_i = 1
			</math>

	=The Script=		=The Script=

Admin: /* Download The Script */

2013-12-19T23:59:27Z

Download The Script

← Older revision		Revision as of 23:59, 19 December 2013
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	=Download The Script=		=Download The Script=

	Download the script here: ~~[[File~~:OneVarCanteraVariableD.py]]		Download the script here: http://charlesmartinreid.com/files/OneVarCanteraVariableD.py

	=References=		=References=

Admin at 23:58, 19 December 2013

2013-12-19T23:58:08Z

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