Finite Difference Methods in CFD

Warda · September 20, 2014, 12:19

Hello every one,
I am new CFD student and I need you help to solve this problem

flotus1 · September 20, 2014, 13:10

So what exactly is your question?

Warda · September 20, 2014, 14:11

I need help to write the second order finite difference discretiation and to find f . thank you

flotus1 · September 20, 2014, 16:50

I guess you mean $-\nabla^2 u = f$

In two-dimensional cartesian coordinates (x and y) this unfolds to

$-\frac{\partial^2 u}{\partial x^2} -\frac{\partial^2 u}{\partial y^2} = f$

The derivatives can now be replaced with some finite difference formula, e.g. second order central differences for node i,j:

$\left. \frac{\partial^2 u}{\partial x^2} \right|_{i,j} = \frac{u_{i-1,j}-2u_{i,j}+u_{i+1,j}}{(\Delta x)^2} + \mathcal{O}(\Delta x^2)$

...solve for $u_{i,j}$

This sounds like some sort of homework so I hope this helps you how to start with it. Just a hint: The task is finding u, not f. f should be given.
From a fluid dynamics point of view, this task is the discretization of the steady flow of an incompressible medium through a circular pipe.
f is the force or pressure gradient (multiplied by some factor) driving the flow while u is the axial velocity.

Warda · September 20, 2014, 23:10

Actually, this is a part of my homework which I'm trying to do, but I'm having great difficulty because I'm not good at math. If you like to help me please explain to me in detail how the solution.

kabilan · September 20, 2014, 23:17

excuse me sir,
in this, you explained ' f ' as diffusive or dp/dx, am i right?
thank you sir.

flotus1 · September 21, 2014, 05:06

I dont feel like doing other peoples homework

And I dont think it would serve any purpose if you copied the solution.

If you show some effort people here will help you with specific problems.
But nobody will write down the full solution for you, especially since solutions to this problem can be found through google.

Warda · September 21, 2014, 12:27

Thank you

September 20, 2014, 12:19	Finite Difference Methods in CFD	#1
Warda New Member British Columbia Join Date: Sep 2014 Posts: 4 Rep Power: 11	Hello every one, I am new CFD student and I need you help to solve this problem Last edited by Warda; September 21, 2014 at 12:32.

September 20, 2014, 16:50		#4
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	I guess you mean $-\nabla^2 u = f$ In two-dimensional cartesian coordinates (x and y) this unfolds to $-\frac{\partial^2 u}{\partial x^2} -\frac{\partial^2 u}{\partial y^2} = f$ The derivatives can now be replaced with some finite difference formula, e.g. second order central differences for node i,j: $\left. \frac{\partial^2 u}{\partial x^2} \right\|_{i,j} = \frac{u_{i-1,j}-2u_{i,j}+u_{i+1,j}}{(\Delta x)^2} + \mathcal{O}(\Delta x^2)$ ...solve for $u_{i,j}$ This sounds like some sort of homework so I hope this helps you how to start with it. Just a hint: The task is finding u, not f. f should be given. From a fluid dynamics point of view, this task is the discretization of the steady flow of an incompressible medium through a circular pipe. f is the force or pressure gradient (multiplied by some factor) driving the flow while u is the axial velocity. Last edited by flotus1; September 20, 2014 at 17:59.

September 21, 2014, 05:06		#7
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	I dont feel like doing other peoples homework And I dont think it would serve any purpose if you copied the solution. If you show some effort people here will help you with specific problems. But nobody will write down the full solution for you, especially since solutions to this problem can be found through google. FMDenaro likes this.

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September 20, 2014, 13:10		#2
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,399 Rep Power: 46	So what exactly is your question?

September 20, 2014, 14:11		#3
Warda New Member British Columbia Join Date: Sep 2014 Posts: 4 Rep Power: 11	I need help to write the second order finite difference discretiation and to find f . thank you

September 20, 2014, 23:10		#5
Warda New Member British Columbia Join Date: Sep 2014 Posts: 4 Rep Power: 11	Actually, this is a part of my homework which I'm trying to do, but I'm having great difficulty because I'm not good at math. If you like to help me please explain to me in detail how the solution.

September 20, 2014, 23:17		#6
kabilan Member kabilan.B Join Date: Jul 2010 Location: chennai Posts: 79 Rep Power: 15	excuse me sir, in this, you explained ' f ' as diffusive or dp/dx, am i right? thank you sir.

September 21, 2014, 12:27		#8
Warda New Member British Columbia Join Date: Sep 2014 Posts: 4 Rep Power: 11	Thank you