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Finite Difference Methods in CFD

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Old   September 20, 2014, 12:19
Default Finite Difference Methods in CFD
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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.
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Old   September 20, 2014, 13:10
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So what exactly is your question?
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Old   September 20, 2014, 14:11
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I need help to write the second order finite difference discretiation and to find f . thank you
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Old   September 20, 2014, 16:50
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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.
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Old   September 20, 2014, 23:10
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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.
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Old   September 20, 2014, 23:17
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excuse me sir,
in this, you explained ' f ' as diffusive or dp/dx, am i right?
thank you sir.
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Old   September 21, 2014, 05:06
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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.
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Old   September 21, 2014, 12:27
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Thank you
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