linearUpwind
 

Hi,

I'm trying to understand the linearUpwind scheme in OpenFOAM. The linearUpwind.C isn't clear to me. So I have some questions:
-Is it simply the extansion of the upwind scheme to the second order?
-In the User Guide, it is said to be first/second order bounded. But for me, I would not have expected it to be bounded in the second order. Where am I wrong?

Thank you.

Yes

It is unbounded unless you use a gradient scheme that bounds the values. Maybe this older discussion will help:

http://www.cfd-online.com/Forums/ope...tedlinear.html

Good luck.

Thank you very much for your answer!

Hi again,

I'm simulating a supersonic flow with a shock, inviscid case.
I wanted to compare a TVD scheme (limitedLinear) with linearUpwind. I tried linearUpwind without cellLimited and then with cellLimited. What I expected was that the linearUpwind scheme without cellLimited gave me spurious oscillations but it doesn't. The two case (linearUpwind with and without cellLimited) gave me the same results. The localisation of the shock isn't very good compare to limitedLinear but I see no spurious oscillations near it.
How can we explain it?

Thank you.

Robin

What type of gradient scheme are you using?

Gauss linear

give your full scheme file. Maybe you can try a leastsquare method.

Here is my fvSchemes for the linearUpwind case without cellLimited:


/*--------------------------------*- C++ -*----------------------------------*\
| ========= | |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |
| \\ / O peration | Version: 2.1.1 |
| \\ / A nd | Web: www.OpenFOAM.org |
| \\/ M anipulation | |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
default Euler;
}

gradSchemes
{
default Gauss linear;
grad(p) Gauss linear;
grad(U) Gauss linear;
}

divSchemes
{
default none;
div(phi,U) Gauss upwind;
div(phid,p) Gauss linearUpwind grad(U);
div(phi,e) Gauss linearUpwind grad(U);
div(phi,K) Gauss linearUpwind grad(U);
div((muEff*dev2(T(grad(U))))) Gauss linear 1;
}

laplacianSchemes
{
default none;
laplacian((rho*(1|A(U))),p) Gauss linear corrected;
laplacian(muEff,U) Gauss linear corrected;
laplacian(alphaEff,e) Gauss linear corrected;
}

interpolationSchemes
{
default linear;
}

snGradSchemes
{
default corrected;
}

fluxRequired
{
default no;
p ;
}


// ************************************************** *********************** //


Thank you, I'll try leastSquare method.

why you didn't put "div(phi,U)" to the second order ?

All the gradient should take the solved variable:

div(phid,p) Gauss linearUpwind grad(p);
div(phi,e) Gauss linearUpwind grad(e);
div(phi,K) Gauss linearUpwind grad(K);

I noticed that for all the inviscid case in the tutorials, sonicFoam never use second order for this term. I've tried a second order but it doesn't improve my solution and gave me more spurious oscillations just after the shock.

Sorry for the mistake, I saw it but forgot to change it for the "linearUpwind without cellLimited" case but I didn't made the mistake for the "linearUpwind with cellLimited" case. So I don't think the mistake come from that. But I just ran the simulation with the corrections, I'll tell you if it changes something.

Thank you

A contribution after 8 years:

J. Guerrero's Finite Volume Method: A Crash introduction's 15th slide gives a succinct explanation for the linearUpwind scheme.

Hi . In the slaid 15, shouldn't it be 3/2 instead of 2/3??