Roy Stogner writes: > > On Thu, 24 Jan 2008, li pan wrote: > > > I've worked with Newton type flow equation. To make it > > sure, I would like to know the exact expression of > > equation in ex13. Can you tell me? > > The system of equations with variables (u,p) is : > (partial u)/(partial t) = - (u * grad)u - div(sigma) > div(u) = 0 > > Where sigma is the stress tensor (normalized to have unit viscosity) > sigma = ((grad(u) + transpose(grad(u)))/2 - pI)
I don't think it should have a 1/2. The stress tensor is typically defined as (see e.g. Panton's fluid mechanics book, http://www.cs.otago.ac.nz/postgrads/alexis/FluidMech/node10.html, http://en.wikipedia.org/wiki/Newtonian_fluid ): sigma = -pI + 2*mu*epsilon(u) where epsilon(u) = (1/2)*(grad(u) + grad(u)^t) is known as the "symmetric part" of the velocity gradient. http://mathworld.wolfram.com/SymmetricMatrix.html Now I think this is confusing because the 2 and the 1/2 always cancel, but whatever, this is how people define things. I agree that this email should be in the introductory comments of ex13, a lot of people have asked the same question. -J ------------------------------------------------------------------------- This SF.net email is sponsored by: Microsoft Defy all challenges. Microsoft(R) Visual Studio 2008. http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
