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 <[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 > > [email protected] > > > 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 > [email protected] > https://lists.sourceforge.net/lists/listinfo/libmesh-users ------------------------------------------------------------------------- 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
