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
