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Why results differs between upwind and vanLeerV

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Old   July 23, 2009, 04:58
Question Why results differs between upwind and vanLeerV
  #1
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Dear community,
I have been experimenting with different schemes for a pipe case, and have been running upwind and vanLeerV for the initial phase for two almost identical cases. A two phase flow w/ alpha = 0.5 with different velocities is used.

In setup 1 I used this setup for div schemes:
divSchemes
{
default none;
div(phia,Ua) Gauss upwind;
div(phib,Ub) Gauss upwind;
div(phib,k) Gauss upwind;
div(phib,epsilon) Gauss upwind;
div(phi,alpha) Gauss limitedLinear01 1;
div((-nuEffa*grad(Ua).T())) Gauss linear;
div((-nuEffb*grad(Ub).T())) Gauss linear;
}
... and for setup 2:
divSchemes
{
default none;
div(phia,Ua) Gauss vanLeerV 1;
div(phib,Ub) Gauss vanLeerV 1;
div(phib,k) Gauss upwind;
div(phib,epsilon) Gauss upwind;
div(phi,alpha) Gauss limitedLinear01 1;
div((-nuEffa*grad(Ua).T())) Gauss linear;
div((-nuEffb*grad(Ub).T())) Gauss linear;
}
But the results from the two setups are quite different, and I believe the only difference in my setup is the different schemes. After 10 seconds, the pipe exit looks very different in the two setups - see attached photos. And it is the vanLeer-case which is "delayed". Does anybody have an explanation to this? I suppose the two schemes should yield the same results?
Attached Images
File Type: jpg pipe_upwind.jpg (29.5 KB, 59 views)
File Type: jpg pipe_vanLeer1.jpg (28.6 KB, 58 views)
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Old   November 10, 2012, 05:55
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  #2
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Claus Meister
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Hallo kjetil,

the difference between upwind and vanLeer is, that vanLeer is a scheme composed of upwind and central differencing. Of course, you can have different results, because upwind is alway first order accurate whereby vanLeer can have second order accuracy - when no step gradients occur. For a better understanding, I recommend to read Versteeg (Chapter about upwind, QUCIK etc.). He does a very good analysis about the different schemes.

Cheers
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