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quarkz August 22, 2011 05:59

Use of upwind scheme for interpolation of u/v

I'm trying to use an upwind scheme for spatial discretization, assuming on a non-staggered grid.

If I need to compute the velocity flux u on the east face, depending on the scheme (e.g. 1st order upwind, QUICK), I will need to interpolate using pts i-1, i, i+1 and maybe i-2 or i+2.

However, what if I need to get the velocity v on the east face?

In a centered scheme, I simply interpolate v(i,j) and v(i+1,j). Does it differs now that I'm using an upwind scheme? I feel that I should still use the centered scheme because v in this case is not the outward flux.

I only use an upwind scheme if I need to get velocity v on the north (vertical) face. Is that so?


harbinyg August 22, 2011 11:08

there seems to be some problems with your question
do you mean the velocities are variable which are to be comput or not ?

if the answer is yes;

then normally you should linearlization your problem, as NS equations are nonlinear; --> the background velocity field are known; if you use collocated grid system, people usually use simple average method to obtain the value on the interface, other methods can also be used;

for the equations after linearation, if you choose segregretd algorithm, then you will not meet the problem you mentioned;

quarkz August 26, 2011 09:02

Thanks for the help harbinyg!

the velocities are variables. However, I am using collocated grid with the variables attached to the cell centers.

I understand that I need to interpolate them to face values.

If I am using an upwind scheme, do I interpolate all u/v values using the upwind scheme?

For e.g, at east face, the u velocity is interpolated using an upwind scheme.

My key question is that do I use the upwind scheme to interpolate the v velocity at the east face as well? since v in this case is not the outward flux...

harbinyg August 26, 2011 12:08

No, the velocity interpolation method is not linked to the schemes you choose ...

quarkz August 26, 2011 17:14

Do you mean for both u and v at the east face?

Because for an upwind scheme, u east face value = u(P) if flow is from left to right, but = u(E) if the opposite, given that:

West ----- P ----- e (face) ----- East

As for v,

Is it the same? Or should I just use central difference?


leflix August 27, 2011 04:53

Hi guys,

Generally one use the same scheme for every components u and v. But it exists some schemes which depend on local conditions and they swicth to some different expressions according these local conditions...
But if you want to use upwind scheme, use it for all components.
What you should know is that for Pe>2 (Pe is the Peclet number) then centered scheme is not appropriated because it will lead to spurious oscillations and the code may diverge. In this case you have to switch to upwind scheme.
So this means that if your flow in mainly x convected dominated the use of upwind scheme should be wise for u velocity while you could keep centered scheme for v.
It is always possibe to do so even if I found it a bit weird.

quarkz August 30, 2011 04:10

Ya, that's sort of what I am thinking as well. tks leflix!

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