- **OpenFOAM**
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- - **Fv scheme**
(*https://www.cfd-online.com/Forums/openfoam/82175-fv-scheme.html*)

Fv schemeDear 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: http://www.OpenFOAM.org | | \\/ M anipulation | | \*---------------------------------------------------------------------------*/ FoamFile { version 2.0; format ascii; class dictionary; object fvSchemes; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // ddtSchemes { default steadyState; } gradSchemes { default Gauss linear; grad(p) Gauss linear; grad(U) Gauss linear; } divSchemes { 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; } laplacianSchemes { 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; } interpolationSchemes { default linear; interpolate(U) linear; } snGradSchemes { default corrected; } fluxRequired { default no; p; } // ************************************************** *********************** // 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. - http://www.cfd-online.com/Wiki/Fluid_dynamics - http://www.cfd-online.com/Wiki/Turbulence_modeling - http://www.cfd-online.com/Wiki/Numerical_methods Could you show me some equation ? Thank you very much. Best regards. Fuji |

In User guide book, I found scheme
http://www.openfoam.com/docs/user/fv...#x20-1050004.4 4.4.1 Interpolation schemes4.4.1.2 Schemes for vector fieldsCentred 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 MUSCL MUSCL 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 schemesScheme 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 schemesDiscretisation 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. Fuji |

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 |

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. |

Bonjour,
aux Francais en Australie ? |

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. - http://www.cfd-online.com/Wiki/Fluid_dynamics - http://www.cfd-online.com/Wiki/Turbulence_modeling - http://www.cfd-online.com/Wiki/Numerical_methods Could you explain clearly for me? Thank a lot Best regards Fuji |

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. |

Thank a lot sleepdeprivation
I will try to use it. Fuji |

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