From: li pan <li76pan@ya...>  20080124 17:34:18

thanx John, there is another point. I read the NavierStokes equation in wiki (http://en.wikipedia.org/wiki/NavierStokes_equations). There is a grad(p) term. But it doesn't appear in the equaiton of ex13. pan  John Peterson <peterson@...> wrote: > You mean how do you linearize it? Newton's method > and iterate > within each timestep. > J > > > li pan writes: > > hi Roy, > > thanx for the explaination. But how did you solve > ((u > > * grad)u, v)_Omega? It's a square term. I heard > there > > are some other methods, streamline, least square > FEM > > ... I would like to hear your comments. > > > > pan > > > > > > > >  Roy Stogner <roystgnr@...> wrote: > > > > > > > > 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) > > > > > > Then the weak form we use in ex13 and ex18, > with > > > test functions (v,q) > > > is: > > > ((partial u)/(partial t), v)_Omega =  ((u * > grad)u, > > > v)_Omega > > > + (sigma, grad v)_Omega + (sigma * n, > v)_dOmega > > > (div(u), q) = 0 > > > > > > In ex13 we use Dirichlet boundaries everywhere, > so v > > > = 0 on the > > > boundary and we drop the dOmega term. > Otherwise, > > > you'd substitute > > > into that term the natural boundary condition: > > > sigma * n = 0 > > > > > > which is actually what David wanted in the > first > > > place. ;) > > > > > > You know, we probably ought to have something > like > > > this in the > > > comments heading examples 13 and 18. "The > > > NavierStokes equations" is > > > definitive enough, but the fact that we > integrate > > > all of sigma > > > (including the pressure term) by parts isn't > set in > > > stone. > > >  > > > Roy > > > > > > > > >  > > > 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/ > > > _______________________________________________ > > > Libmeshusers mailing list > > > Libmeshusers@... > > > > > > https://lists.sourceforge.net/lists/listinfo/libmeshusers > > > > > > > > > > > > ____________________________________________________________________________________ > > Be a better friend, newshound, and > > knowitall with Yahoo! Mobile. Try it now. > http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ > > > > > > > >  > > 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/ > > _______________________________________________ > > Libmeshusers mailing list > > Libmeshusers@... > > > https://lists.sourceforge.net/lists/listinfo/libmeshusers > ____________________________________________________________________________________ Looking for last minute shopping deals? Find them fast with Yahoo! Search. http://tools.search.yahoo.com/newsearch/category.php?category=shopping 