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fuji November 18, 2010 23:45

Fv scheme
Dear all
I am a newbie on OpenFoam software, so i want to ask about fv scheme

Case name PitzDaily, located in the OpenFoam_Tutorial/ simpleFoam directory

/*--------------------------------*- C++ -*----------------------------------*\
| ========= | |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |
| \\ / O peration | Version: 1.5 |
| \\ / A nd | Web: |
| \\/ M anipulation | |
version 2.0;
format ascii;
class dictionary;
object fvSchemes;
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

default steadyState;

default Gauss linear;
grad(p) Gauss linear;
grad(U) Gauss linear;

default none;
div(phi,U) Gauss upwind;
div(phi,k) Gauss upwind;
div(phi,epsilon) Gauss upwind;
div(phi,R) Gauss upwind;
div(R) Gauss linear;
div(phi,nuTilda) Gauss upwind;
div((nuEff*dev(grad(U).T()))) Gauss linear;

default none;
laplacian(nuEff,U) Gauss linear corrected;
laplacian((1|A(U)),p) Gauss linear corrected;
laplacian(DkEff,k) Gauss linear corrected;
laplacian(DepsilonEff,epsilon) Gauss linear corrected;
laplacian(DREff,R) Gauss linear corrected;
laplacian(DnuTildaEff,nuTilda) Gauss linear corrected;

default linear;
interpolate(U) linear;

default corrected;

default no;

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

I don't know about some equation as: steadyState, Gauss linear, Gauss upwind, Gauss linear corrected, Euler, ...

Could you explain clearly for me?
I found all of equation in the Cfd online. But i didn't see it.

Could you show me some equation ?
Thank you very much.

Best regards.

fuji November 19, 2010 00:14

In User guide book, I found scheme

4.4.1 Interpolation schemes Schemes for vector fields

Centred schemes
+ linear Linear interpolation (central differencing)
+ cubicCorrection Cubic scheme
+ midPoint Linear interpolation with symmetric weighting

Upwinded convection schemes
+ upwind Upwind differencing
+ linearUpwind Linear upwind differencing
+ skewLinear Linear with skewness correction
+ QUICK Quadratic upwind differencing

TVD schemes
limitedLinear limited linear differencing
vanLeer van Leer limiter
limitedCubic Cubic limiter

NVD schemes
SFCD Self-filtered central differencing
Gamma Gamma differencing

Table 4.6: Interpolation schemes.
4.4.2 Surface normal gradient schemes

Scheme Description
corrected Explicit non-orthogonal correction
uncorrected No non-orthogonal correction
limited Limited non-orthogonal correction
bounded Bounded correction for positive scalars
fourth Fourth order

Table 4.7: Surface normal gradient schemes.

4.4.3 Gradient schemes

Discretisation scheme Description
Gauss <interpolationScheme> Second order, Gaussian integration
leastSquares Second order, least squares
fourth Fourth order, least squares
cellLimited <gradScheme> Cell limited version of one of the above schemes
faceLimited <gradScheme> Face limited version of one of the above schemes


I don't understand about it. Can you help me, Please!

Thank you very much.

julien.decharentenay November 19, 2010 00:40

Hi Fuji,

You probably should narrow down your question. Below are a few quick answer

steadyState: The temporal term in the appropriate equation is neglected (i.e steady state solution which does not evolve in time). It is usually replaced by a under-relaxation terms to reduce the stiffness of the system;

Gauss: is a method involving the Gauss theorem, which transform a volume integral into a surface integral;

Gauss linear: apply the gauss theorem, using a linear interpolation of the cell center value to the face value;

Gauss upwind: apply the gauss theorem, using an upwind interpolation of the cell center value to the face value.

I am not sure if the above is really useful, but it is my definition of these terms.

Good luck.

julien.decharentenay November 19, 2010 00:42

Forgot, I was meaning to point you to the cfd-online Wiki>Reference Section>Numerical Method.

It could be a good start to understand the meaning behind these terms.

olivier78 November 19, 2010 22:16

aux Francais en Australie ?

fuji November 21, 2010 23:20

Dear Julien

Thank you for your reply.
But I have still understood fv scheme.
In cfd-online Wiki>Reference Section>Numerical Method

I found all of equation in the Cfd online. But i didn't see it.
Could you explain clearly for me?

Thank a lot

Best regards

sleepdeprivation November 22, 2010 07:15

PDE's (the equations OpenFOAM solves) are equations of derivatives. The schemes are different ways to approximate those derivatives.
In finite difference equations, you classically make a Taylor series expansion then solve for the derivative you want (like d/dx).
Finite volume (what OpenFOAM uses) is similar, but cell based so you can use Gauss's Theorem and flux terms.

Many of the schemes are specific to CFD, so if you want information about something specific, check out the source code, just various places on the internet, or even Journal Articles if you want a really deep understanding.

If you're really confused, check out a calculus book, or one on numerical methods.

fuji December 13, 2010 23:44

Thank a lot sleepdeprivation
I will try to use it.


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