Tensor in cylindrical coordinate system

Onurb · December 1, 2020, 12:58

Hello,

I am solving the following equation:

$\frac{\partial c}{\partial t} +\nabla \cdot ( \textbf{u}c) - \nabla (\textbf{D}\cdot \nabla c) = 0$

with $\textbf{D}$ given by

$\textbf{D}_{xyz} = \left[ \stackrel{D_{xx}}{\stackrel{0}{0}} \quad \stackrel{0}{\stackrel{D_{yy}}{0}} \quad \stackrel{0}{\stackrel{0}{D_{zz}}}\right]$

Using OpenFOAM I defined the tensor $\textbf{D}$ as

Code:

volScalarField Dxx( Dm + lxx*mag(U) );
volScalarField Dyy( Dm + lyy*mag(U) );
volScalarField Dyy( Dm + lzz*mag(U) );

symmTensor Txx(1,0,0,0,0,0);
symmTensor Tyy(0,0,0,1,0,0);
symmTensor Tzz(0,0,0,0,0,1);

  volSymmTensorField D = Dxx*Txx + Dyy*Tyy + Dzz*Tzz;

However, I'm in doubt about how to handle the problem with tensor in the cylindrical coordinate system (attached figure)

$\textbf{D}_{r\theta z} = \left[ \stackrel{D_{rr}}{\stackrel{0}{0}} \quad \stackrel{0}{\stackrel{D_{\theta\theta}}{0}} \quad \stackrel{0}{\stackrel{0}{D_{zz}}}\right]$

I would like to know how implement in OF the transformation $\textbf{D}_{r\theta z} \quad to \quad \textbf{D}_{xyz}$ , in other words, I use as input $D_{rr}, D_{\theta\theta}, D_{zz}$ and internally OF transform to $D_{xx}, D_{yy}, D_{zz}$

olesen · December 5, 2020, 04:19

You should take a look at the coordinate system classes,but make sure you are using OpenFOAM-v1812 or newer.
To have the correct result, in cylindrical coordinates you will also need to provide the locations where the transformation occurs. You can have a single tensor transformed at all of the locations, or supply locations and tensors. The field of positions can also be an indirect list etc, so only for a zone etc.
Unfortunately, since there are so many variants of transforms the corresponding methods in coordinateSystem are wrapped in macros - better for code maintenance (ie, programmer sanity), but horrible to read as a user. Probably best to look at the extracted documentation when picking your method.

https://www.openfoam.com/documentati...ateSystem.html

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December 5, 2020, 04:19		#2
olesen Senior Member Mark Olesen Join Date: Mar 2009 Location: https://olesenm.github.io/ Posts: 1,714 Rep Power: 40	You should take a look at the coordinate system classes,but make sure you are using OpenFOAM-v1812 or newer. To have the correct result, in cylindrical coordinates you will also need to provide the locations where the transformation occurs. You can have a single tensor transformed at all of the locations, or supply locations and tensors. The field of positions can also be an indirect list etc, so only for a zone etc. Unfortunately, since there are so many variants of transforms the corresponding methods in coordinateSystem are wrapped in macros - better for code maintenance (ie, programmer sanity), but horrible to read as a user. Probably best to look at the extracted documentation when picking your method. https://www.openfoam.com/documentati...ateSystem.html