nonNewtonianFluidFoam  no grad(nu) & grad(U)
Hello folks,
does anybody know why in this solver no grad(nu) & grad (U) is taken into account in Ueqn? In interFoam one finds fvVectorMatrix UEqn ( fvm::ddt(rho, U) + fvm::div(rhoPhi, U)  fvm::laplacian(muEff, U)  (fvc::grad(U) & fvc::grad(muEff)) ); due to the fact that muEff is variable in space. In nonNewtonianIcoFoam  (fvc::grad(U) & fvc::grad(muEff)) is ignored. Thanks for replies. 
Answer: continuum mechanics
Hello there
the additional term " (fvc::grad(U) & fvc::grad(muEff))" is correct and is now present in nonNewtoninanIcoFoam in the OpenFOAM 2.1.x. You can also see this term in the interFoam solver. If you are only used to standard fluid mechanics, you will be puzzled by this term. If you want to understand the physical reason for this term, you have to go into continuum mechanics. My favourite book about the subject is... G. E. Mase. Schaums Outline Series: Theory and Problems of Continuum Mechanics. McGrawHill Inc., USA, 1970. Hope this helps J. 
Hello Jon,
thank you for your answer. I just wondered why this term was missing in the solver I used so far (v.1.6ext). I actually thought it was missing. I recently found out that you reported this bug in April. Thanks a lot, janto 
sorry, apparantly I was reading your post too fast,...
good luck,... J. 
Excuse me, where can I download this book?
Theory and Problems of Continuum Mechanics 
You have to buy the book (I dont know of any download). But it is cheep. :)
See for example: http://www.amazon.com/SchaumsOutlin...mechanics+mase Quote:

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This book is not on sell in our country. Do you have another articles? Thanks. 
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There is another book I use : L. E. Malvern. Introduction to the Mechanics of Continuous Medium. PrenticeHall, Inc., USA, 1969. ...but that book is much more expensive :( The only thing I can suggest if you have to download is search by using the string: "continuum mechanics pdf" hope this help Cheers Jon 
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I still cant get out why there is (fvc::grad(U) & fvc::gradfluid.nu()). It exists in nonnewtonianIcoFoam and interFoam. Who can give me a hint pls?

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Hi,
maybe this picture helps: Attachment 26578 The first term is equivalent with eta*laplace(v). Regards, Janto 
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You mean [LaTeX Error: Syntax error] Why shouldnt it be: [LaTeX Error: Syntax error] 
Hello Forrest,
you would be right if the viscosity was constant all over the domain. However, in interFoam and nonNewtonianIcoFoam the viscosity is a field variable (have a look in createFields where the viscosity is defined) and depends therefore on the spatial coordinates. Owing to that the gradient of the viscosity does not vanish. 
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Hello Sharonyue
Here is something I did in haste (there might be some typo errors, like vector arrow symbol missing over the velocity U), but basically this is the approach. You would not use array approach as you showed earlier, but rather directly work with dyads and vectors directly. Such is much easier. I hope you can use this document, but you need to know continuum mechanics,... there is no way around it, if you are going to do serious CFD work. Cheers and good luck Jon 
NEAT!!!
To Janto Quote:
To Jon: Wonderful, It helps me a lot!! Thank you both very much! 
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