From: John Peterson <peterson@cf...>  20070824 19:15:54

Forwarded from Ben Kirk to libmeshusers. Benjamin Kirk writes: > John, Derek  NASA is blocking me from a direct post to the libmesh mailing > list. I'll trust you to forward this along... > > In short, yes. Take a look in ~benkirk/phd/code/s3.implicit/src/* in the > cfdlab. > > The formulation of interest is denoted rbm_medale and used Mark Medale's > pressure projection method for the RayleighBenardMarangoni problem. > > I seriously doubt that the code compiles right now, but the gist is as > follows: > >  three systems are used for flow, pressure, and temperature, respectively. >  the momentum system is updated using an old pressure >  a possion problem is solved for pressure >  the momentum is updated using this pressure such that div(u)=0 >  the thermal system is then solved. > > > The rough idea is this: > > (U_new  U_old)/dt = (grad(P) + N(U_new)) > > is replaced by > > (U_*  U_old)/dt = N(U_*) > (U_new  U_*)/dt = grad(P) > > Note that if you add them you kinda get the original PDE back. > > Now, >  solve for U_* >  solve div(grad(P) = div(U_new  U_*)/dt =  div(U_*)/dt > since we require div(U_new)=0 >  solve (mass matrix projection) U_new = U_*  dt*grad(P) > Barring any algebra mistakes. > > The code probably will not compile (it is from January 2004) but you can see > all the elements in there. > > Ben > > > > On 8/24/07 1:09 PM, "John Peterson" <peterson@...> wrote: > > > spdomin writes: > >> Greetings, > >> > >> Has anyone coded an equal order, low Mach number, i.e., acoustically > >> incompressible, pressure projection algorithm within libMesh? If so, I would > >> be very interested to learn more about the details of the libMesh > >> implementation. > >> > > > > I don't believe so, but I could be mistaken. Does the equalorder > > interpolation > > require stabilization of some type? Do you have a reference for the scheme > > you speak of? I might be able to take a quick glance and see if there's > > anything which would make it impossible or difficult to do in the current > > library. > > > > J 