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 <[EMAIL PROTECTED]> 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 > Navier-Stokes 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/ > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/libmesh-users > ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all 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/ _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
