Solving a Laplace equation for a scalar quantity

ali hemmati · July 13, 2011, 04:40

Hello,

I am trying to solve $\nabla^{2}\varphi=0$ , i.e. homogeneous Laplace equation, in which $\varphi$ is a scalar quantity and is described in a zone(2D or 3D). We know boundary values of $\varphi$ in borders of the zone. This problem is very analogous to head conduction at steady state, yet $\varphi$ is the electric potential here, not temperature.

I am wondering how to implement this problem in FLUENT. I think I have to mesh the zone and use a udf or something like that.

Thanks for your help.

Amir · July 13, 2011, 07:40

Hi Ali,
you can easily do that by implementing a UDS, user defined scalar; in it's definition, ignore unsteady and convective terms.

Amir

Clarence91 · October 2, 2014, 11:05

Hi Amir,

Can you elaborate your statement? How can we justify that unsteady and convective terms can be ignored for solving the laplace equation? (i need to find the change in electric field in my geometry)
I think you know how my geometry looks like :P , I have to find the electric field in the rotor domain.
If possible can you share the UDF with me?

Thank you.
-Mark

Amir · October 2, 2014, 13:34

Quote:

Originally Posted by Clarence91

Hi Amir,

Can you elaborate your statement? How can we justify that unsteady and convective terms can be ignored for solving the laplace equation? (i need to find the change in electric field in my geometry)
I think you know how my geometry looks like :P , I have to find the electric field in the rotor domain.
If possible can you share the UDF with me?

Thank you.
-Mark

Dear Mark,

"UDS" is "User-Defined Scalar" equation and is available in FLUENT, something like energy equation and totally different from "UDF"! In the process of enabling a UDS, you can manage the unsteady and convective terms. For more info, please refer to the manual.

Bests,

Tharanga · February 11, 2015, 19:56

Hi,
Can we solve defined scalar in x, y, z direction separately (for 3D geometry) or how can we see the scalar values in x y z directions using post processing?
Regards
Tharanga

Amir · February 12, 2015, 04:02

Quote:

Originally Posted by Tharanga

Hi,
Can we solve defined scalar in x, y, z direction separately (for 3D geometry) or how can we see the scalar values in x y z directions using post processing?
Regards
Tharanga

Hi,
For sure you cannot solve it separately, but if you want to see the scalar values in a specified direction, you can simply draw a line and plot the scalar values over it...

Bests,

Tharanga · February 12, 2015, 05:08

Hey, Thank you for the reply. I have solved the laplace eq (3D) and I need to get surface integration over x y z direction (separately) . Is there any method for that? cheers

Tharanga · February 12, 2015, 05:12

If I elaborate more, I cant choose from the drop down menu x-scalar values etc. Therefore, I'm struggling to find x y z values over a surface. Thank you.

pakk · February 12, 2015, 05:24

With a user defined scalar, you calculate a scalar, not a vector.
A scalar does not have a x-component... So your question does not make any sense.

If you solved an electrostatic problem, your scalar is probably the electric potential. Which component do you want? The x-component of the electric field? You should know the relation between those two.

Tharanga · February 12, 2015, 05:36

It is a homogenized flow problem. Ultimately, I need to solve laplace eqn (vector) with BC's . Yes, you are right but there is no other way (I think) than UDS method in fluent to solve Laplace. Please suggest me an alternative method. Thank you

pakk · February 12, 2015, 06:00

You don't make clear why you need another way. What is wrong with the UDS method?

And are you sure you want a vector laplace equation??? That is very unusual. I don't know why a "homogenized flow problem" would lead to a vector variant of the laplace equation.

Tharanga · February 16, 2015, 20:42

Hi, Thank you very much for your kind replies. I solved it as three different problems in fluent. I got the results.

Regards,
Tharanga

July 13, 2011, 04:40	Solving a Laplace equation for a scalar quantity	#1
ali hemmati New Member Ali Join Date: Mar 2011 Posts: 27 Rep Power: 14	Hello, I am trying to solve $\nabla^{2}\varphi=0$ , i.e. homogeneous Laplace equation, in which $\varphi$ is a scalar quantity and is described in a zone(2D or 3D). We know boundary values of $\varphi$ in borders of the zone. This problem is very analogous to head conduction at steady state, yet $\varphi$ is the electric potential here, not temperature. I am wondering how to implement this problem in FLUENT. I think I have to mesh the zone and use a udf or something like that. Thanks for your help.

July 13, 2011, 07:40		#2
Amir Senior Member Amir Join Date: May 2009 Location: Montreal, QC Posts: 735 Blog Entries: 1 Rep Power: 22	Hi Ali, you can easily do that by implementing a UDS, user defined scalar; in it's definition, ignore unsteady and convective terms. Amir ali hemmati likes this.

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October 2, 2014, 11:05		#3
Clarence91 Member MarkClarence Join Date: Jul 2014 Posts: 32 Rep Power: 10	Hi Amir, Can you elaborate your statement? How can we justify that unsteady and convective terms can be ignored for solving the laplace equation? (i need to find the change in electric field in my geometry) I think you know how my geometry looks like :P , I have to find the electric field in the rotor domain. If possible can you share the UDF with me? Thank you. -Mark

February 11, 2015, 19:56		#5
Tharanga New Member Tharanga Jayathungage Don Join Date: Sep 2014 Location: Auckland Posts: 25 Rep Power: 10	Hi, Can we solve defined scalar in x, y, z direction separately (for 3D geometry) or how can we see the scalar values in x y z directions using post processing? Regards Tharanga

February 12, 2015, 05:08		#7
Tharanga New Member Tharanga Jayathungage Don Join Date: Sep 2014 Location: Auckland Posts: 25 Rep Power: 10	Hey, Thank you for the reply. I have solved the laplace eq (3D) and I need to get surface integration over x y z direction (separately) . Is there any method for that? cheers

February 12, 2015, 05:12		#8
Tharanga New Member Tharanga Jayathungage Don Join Date: Sep 2014 Location: Auckland Posts: 25 Rep Power: 10	If I elaborate more, I cant choose from the drop down menu x-scalar values etc. Therefore, I'm struggling to find x y z values over a surface. Thank you.

February 12, 2015, 05:24		#9
pakk Senior Member Join Date: Nov 2013 Posts: 1,965 Rep Power: 25	With a user defined scalar, you calculate a scalar, not a vector. A scalar does not have a x-component... So your question does not make any sense. If you solved an electrostatic problem, your scalar is probably the electric potential. Which component do you want? The x-component of the electric field? You should know the relation between those two.

February 12, 2015, 05:36		#10
Tharanga New Member Tharanga Jayathungage Don Join Date: Sep 2014 Location: Auckland Posts: 25 Rep Power: 10	It is a homogenized flow problem. Ultimately, I need to solve laplace eqn (vector) with BC's . Yes, you are right but there is no other way (I think) than UDS method in fluent to solve Laplace. Please suggest me an alternative method. Thank you

February 12, 2015, 06:00		#11
pakk Senior Member Join Date: Nov 2013 Posts: 1,965 Rep Power: 25	You don't make clear why you need another way. What is wrong with the UDS method? And are you sure you want a vector laplace equation??? That is very unusual. I don't know why a "homogenized flow problem" would lead to a vector variant of the laplace equation.

February 16, 2015, 20:42		#12
Tharanga New Member Tharanga Jayathungage Don Join Date: Sep 2014 Location: Auckland Posts: 25 Rep Power: 10	Hi, Thank you very much for your kind replies. I solved it as three different problems in fluent. I got the results. Regards, Tharanga