FVM Exercise that I cant resolve

Breynolds · May 25, 2016, 20:23

Hi everyone

Mi name is Brian and I´m studying mechanical engineer, I have a problem of finite volume method that I cant resolve, (please see attach)

exercise says that interpolation of a transported variable (phi) en face w, it could be express like

(phi)w = Aww(phi)ww+Aw(phi)w+Ap(phi)p

I need to find Aww, Aw and Ap for the next schemes:

Upwind First order
CDS
Second order Upwing
QUICK

Anybody can help me PLEASE with this problem??? thank you

LUQILIN · May 25, 2016, 21:20

Just a simple Taylor expansion. You can it in any CFD test books.

arjun · May 26, 2016, 00:28

Quote:

Originally Posted by Breynolds

Hi everyone

Mi name is Brian and I´m studying mechanical engineer, I have a problem of finite volume method that I cant resolve, (please see attach)

exercise says that interpolation of a transported variable (phi) en face w, it could be express like

(phi)w = Aww(phi)ww+Aw(phi)w+Ap(phi)p

I need to find Aww, Aw and Ap for the next schemes:

Upwind First order
CDS
Second order Upwing
QUICK

Anybody can help me PLEASE with this problem??? thank you

Take this as an example

In case of first order upwind, (phi)e as interpolated value

(phi)e = (phi)W

So you have

(phi)e = 0 . (phi)ww+ 1 . (phi)W+ 0 .(phi)P

Aww = 0
Aw = 1
Ap = 0

Now do the same for others.

FMDenaro · May 26, 2016, 03:34

First order upwind is just a constant value taken in the upwind direction, CDS is a linear interpolation and quadratic polynomial is used for the second order upwind..
The problem is in the QUICK, if you are working in a 2D case, the scheme of Leonard is based on the integral of the 2D polynomial that is done analytically along the face. You need to work on a multidimensional stencil.

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May 25, 2016, 21:20		#2
LUQILIN Member LUQILIN Join Date: May 2016 Location: Harbin, China Posts: 35 Rep Power: 9	Just a simple Taylor expansion. You can it in any CFD test books.

May 26, 2016, 03:34		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	First order upwind is just a constant value taken in the upwind direction, CDS is a linear interpolation and quadratic polynomial is used for the second order upwind.. The problem is in the QUICK, if you are working in a 2D case, the scheme of Leonard is based on the integral of the 2D polynomial that is done analytically along the face. You need to work on a multidimensional stencil.