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Old   June 12, 2012, 09:51
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Edward Leonard
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Quote:
Originally Posted by grtabor View Post
Its to do with the discretisation of the

U & fvc::grad(T)

term. In the FVM we discretise this using Gauss theorem, converting it into fluxes into and out of the domain. If we discretise the term written like this then it is not guaranteed to preserve conservation of the quantity being advected (here essentially the energy); i.e. your derivative may be loosing or gaining energy. If you do some manipulation of the term to get it into the form

fvc::div(phi, T)

where phi is essentially the same as U, then when we apply Gauss we get something which preserves continuity at the _numerical_ level, rather than the mathematical level. This would be a strong conservative implementation.

Gavin
Forgive my lack of mathematical background, but is there someone that would be able to show the manipulation steps such that
\vec{U}\cdot\nabla\vec{U}=\nabla\cdot(\phi\vec{U}) where \phi=\vec{U}\cdot\vec{S}_f?
I've taken a few whacks at it and my lack of FVM, I think, is making me miss some obvious connection.

Many thanks to whomever is able to assist me!

Edit: Nevermind. Figured it out. Odd way, though it works.

Last edited by iamed18; June 15, 2012 at 09:47. Reason: added definition of [MATH]\phi[/MATH], figured it out.
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ddt, lagrangian derivative

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