strainrate()

sharonyue · September 23, 2013, 04:18

Hi guys,

This is a piece of code in viscosity.C

Code:

Foam::tmp<Foam::volScalarField> Foam::viscosityModel::strainRate() const
{
    return sqrt(2.0)*mag(symm(fvc::grad(U_)));
}

Mathematically, it is $\gamma = \sqrt 2 \cdot \left| {\frac{1}{2}\left( {\nabla u + \nabla {u^T}} \right)} \right|$

but how can I get the magnitude of a tensor? and why isn't this strainrate a tensor but a scalar? Shouldnt it be:

Code:

Foam::tmp<Foam::volTensorField> Foam::viscosityModel::strainRate() const
{
    return symm(fvc::grad(U_));
}

vonboett · September 24, 2013, 03:27

mag(D) = sqrt(D_ij D_ij ) = norm of strain rate tensor in OpenFOAM, where D_ij = 1/2 ((grad(U)+grad(U)^T) = symm(grad(U)) = 2*DR and that is a scalar. There are several definitions of the norm, this is one wideley used to calculate a kind of "magnitude" of the tensors components

sharonyue · September 26, 2013, 03:41

Quote:

Originally Posted by vonboett

mag(D) = sqrt(D_ij D_ij ) = norm of strain rate tensor in OpenFOAM, where D_ij = 1/2 ((grad(U)+grad(U)^T) = symm(grad(U)) = 2*DR and that is a scalar.

Sorry. Are you sure this is a scalar?

vonboett · September 30, 2013, 09:35

Sorry, more precise: norm(D) = sqrt{trace(D^2)}, so if I am correct Dij above would be: Dij = 0.5*(du_i/dx_j + du_j/dx_i) + 0.5(du_i/dx_j - du_j/dx_i).
Please check if I messed with the indices, du_/dx_ stands for the corresponding derivative of the velocity.

September 23, 2013, 04:18	strainrate()	#1
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 838 Rep Power: 17	Hi guys, This is a piece of code in viscosity.C Code: Foam::tmp<Foam::volScalarField> Foam::viscosityModel::strainRate() const { return sqrt(2.0)mag(symm(fvc::grad(U_))); } Mathematically, it is $\gamma = \sqrt 2 \cdot \left\| {\frac{1}{2}\left( {\nabla u + \nabla {u^T}} \right)} \right\|$ but how can I get the magnitude of a tensor? and why isn't this strainrate a tensor but a scalar? Shouldnt it be: Code: Foam::tmp<Foam::volTensorField> Foam::viscosityModel::strainRate() const { return symm(fvc::grad(U_)); } Last edited by sharonyue; September 26, 2013 at 04:16.*

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September 24, 2013, 03:27		#2
vonboett Senior Member Albrecht vBoetticher Join Date: Aug 2010 Location: Zürich, Swizerland Posts: 237 Rep Power: 16	mag(D) = sqrt(D_ij D_ij ) = norm of strain rate tensor in OpenFOAM, where D_ij = 1/2 ((grad(U)+grad(U)^T) = symm(grad(U)) = 2*DR and that is a scalar. There are several definitions of the norm, this is one wideley used to calculate a kind of "magnitude" of the tensors components

September 30, 2013, 09:35		#4
vonboett Senior Member Albrecht vBoetticher Join Date: Aug 2010 Location: Zürich, Swizerland Posts: 237 Rep Power: 16	Sorry, more precise: norm(D) = sqrt{trace(D^2)}, so if I am correct Dij above would be: Dij = 0.5*(du_i/dx_j + du_j/dx_i) + 0.5(du_i/dx_j - du_j/dx_i). Please check if I messed with the indices, du_/dx_ stands for the corresponding derivative of the velocity.