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Magnitude of the strain tensor

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Old   June 15, 2007, 09:37
Default Hi FOAMers, I would like to
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Max
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Hi FOAMers,

I would like to have your opinion about the following problem:

- the strain tensor is defined as

S = 2 * symm(grad(U)) = grad(U) + grad(U)^T (1)

- and, according to the linear algebra, its magnitude is

|S| = sqrt(.5 * (S_ij * S_ij)) (2)

- now, if I let OpenFOAM to write out both the U gradients and S

S = mag(2*symm(fvc:grad(U))) (3)

I see that values coming from (3) and (2) (calculated manually) are different.

I had a look to the vectorSpace class and what I can understand (with my little C++ knowledge), is that the magnitude of a tensor S is given by

|S| = sqrt(Sij * Sij) (4)

which differs from Eq. (2). Additionally, a manual check with the help of Eq.(4) does not return what is given by OF (Eq. (3)) and there is not any constant factor between their values...

What am I missing?

Thanks a lot,
Massimiliano
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Old   August 7, 2011, 03:02
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Claus Meister
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Hello Foamer,

strain rate Tensor is defined by

S:=1/2 [ grad(U)+gard(U)^T]

Try it and give me respond if it's worked.

Cheers
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