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Mathematical background for discretisation schemes

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Old   February 7, 2018, 13:22
Default Mathematical background for discretisation schemes
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Ladferror
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Hello everyone,

at the moment I'm writing my masters thesis about simulating turbulent flows and we chose to do the simulations in OpenFOAM. Since I study mathematics, it would be important for me to also explain how discretization schemes are applied to the equations which are going to be solved numerically.

For example I am using the pimpleFoam solver (for simulating the Kármán vortex street) and I would like to explain the "Gauss linear" scheme of gradSchemes in the fvSchemes file by applying it e.g. on the Reynolds-Averaged-Navier-Stokes-Equations by hand (in the file "turbulenceProperties" the simulationType is set to RAS). I looked it up in the UserGuide of OpenFOAM (where it is explained briefly but I wasn't able to understand it properly) and tried to find it online but I haven't found where this is explained.

Therefore I wanted to ask, if there is some kind of documentation or some place where I could look it up, without looking through the program code.

I wasn't sure where to post this or if there is a similar post, where this was already asked.

Thank you for you answers.
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Old   February 11, 2018, 13:05
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Santiago Lopez Castano
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Quote:
Originally Posted by Ladferror View Post

Hello everyone,

at the moment I'm writing my masters thesis about simulating turbulent flows and we chose to do the simulations in OpenFOAM. Since I study mathematics, it would be important for me to also explain how discretization schemes are applied to the equations which are going to be solved numerically.

For example I am using the pimpleFoam solver (for simulating the Kármán vortex street) and I would like to explain the "Gauss linear" scheme of gradSchemes in the fvSchemes file by applying it e.g. on the Reynolds-Averaged-Navier-Stokes-Equations by hand (in the file "turbulenceProperties" the simulationType is set to RAS). I looked it up in the UserGuide of OpenFOAM (where it is explained briefly but I wasn't able to understand it properly) and tried to find it online but I haven't found where this is explained.

Therefore I wanted to ask, if there is some kind of documentation or some place where I could look it up, without looking through the program code.

I wasn't sure where to post this or if there is a similar post, where this was already asked.

Thank you for you answers.
The book on CFD by Ferziger and Peric is a good start if interested in the algebraic details of FVM. As for a more mathematical-oriented text, i would recommend the book of peter wesseling on CFD, although is kind of encyclopedic for my taste
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Old   February 11, 2018, 17:01
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Quote:
Originally Posted by Ladferror View Post

Hello everyone,

at the moment I'm writing my masters thesis about simulating turbulent flows and we chose to do the simulations in OpenFOAM. Since I study mathematics, it would be important for me to also explain how discretization schemes are applied to the equations which are going to be solved numerically.

For example I am using the pimpleFoam solver (for simulating the Kármán vortex street) and I would like to explain the "Gauss linear" scheme of gradSchemes in the fvSchemes file by applying it e.g. on the Reynolds-Averaged-Navier-Stokes-Equations by hand (in the file "turbulenceProperties" the simulationType is set to RAS). I looked it up in the UserGuide of OpenFOAM (where it is explained briefly but I wasn't able to understand it properly) and tried to find it online but I haven't found where this is explained.

Therefore I wanted to ask, if there is some kind of documentation or some place where I could look it up, without looking through the program code.

I wasn't sure where to post this or if there is a similar post, where this was already asked.

Thank you for you answers.
Hello

1) An Introduction to Computational Fluid Dynamics by "H K Versteeg and W Malalasekera"

2) The Finite Volume Method in Computational Fluid Dynamics (An Advanced Introduction with OpenFOAM and Matlab) by " F. Moukalled L. Mangani M. Darwish"
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