From: John Peterson <peterson@cf...>  20070404 15:09:30

Luca Antiga writes: > Hi, > > One thing that seemed to help a bit (at least in 2D) was to use the > > "lumped" L2 projection (e.g. ex13). If memory serves, that solution > > "looked" slightly better (at least in 2D). > We confirm that this helps also in 3D. We'll show you images as soon > as Lorenzo is around. > The situation changes sensibly, you see much fewer nonzero vectors > on the noslip faces. > > Ultimately we'll work with blood vessels, so we won't have > discontinuous boundary conditions. > However, I can tell you that we tried on a vessel with parabolic > inlet conditions (that go to zero > at the wall, so no discontinuity). With L2 boundary conditions, the > first ring of refined nodes on the > noslip side wall connected to the inlet face had nonzero velocity > vectors pointing opposite > to the inlet flow direction. Hmm... and the lumped L2projection looks slightly better than that? I will try implementing the "pinwheel" type forcing function for the Stokes problem with homogeneous zero Dirichlet BCs in 2D using adaptivity, and see what that gives us. > >> Yes, but then Gibbs' type ringing usually is large. What's worse: as > >> you refine the mesh the boundary condition approximation will > >> converge > >> in the L2 norm, but it can't converge in L_infinity.. > > I don't know the details, so I'm not sure it makes sense, but it > looks to me like the presence and size of > overundershoots depends on the size of the coarselevel mesh. Could > this be related to the way > hanging node constraints are handled (L2)? > Just to get more insight: will a uniformly AMR refined mesh behave > differently than a nonrefined > mesh with the same sized elements as the fine AMR ones? How much of > an influence will the coarselevel > mesh have? It shouldn't depend on what mesh you start with, unless it was coarse enough to have Galerkininstability type oscillations. In that case, local cellReynolds number violations can cause over/undershoots (for NavierStokes obviously, not Stokes flow). In answer to your second question, a "uniformlyrefined AMR mesh" should behave identically to a nonrefined mesh with the same size elements. I would be interested in seeing a case where it does not, if you have one. J > Thanks a lot for your time > > Luca > >  > Luca Antiga, PhD > Head, Medical Imaging Unit, > Bioengineering Department, > Mario Negri Institute > email: antiga@... > web: http://villacamozzi.marionegri.it/~luca > mail: Villa Camozzi, 24020, Ranica (BG), Italy > phone: +39 035 4535381 > > > On Apr 4, 2007, at 4:22 PM, John Peterson wrote: > > > Roy Stogner writes: > >> On Wed, 4 Apr 2007, Luca Antiga wrote: > >> > >>> I could live with non zero values on the zero velocity faces, but > >>> aren't > >>> those a bit large (10% of the top face velocity)? > >> > >> Yes, but then Gibbs' type ringing usually is large. What's worse: as > >> you refine the mesh the boundary condition approximation will > >> converge > >> in the L2 norm, but it can't converge in L_infinity.. > >> > >>> I'm just worried that the situation might go out of control in > >>> complicated geometries, so that's why I'm a bit picky on this > >>> problem. > >> > >> It's not the geometry that's controlling the problem, it's the > >> discontinuity in the boundary conditions. > > > >> I think John's had somewhat smoother results by using an H1 instead > >> of L2 boundary penalty, but when you try to force a continuous > >> approximation function to take on discontinuous values, there's > >> really no good way for it to react. > > > > Actually, I couldn't get the H1 projection to work (in 2D). I tried > > penalizing the tangential derivatives, to e.g. enforce du/dx=dv/dx=0 > > along the lid. > > > > One thing that seemed to help a bit (at least in 2D) was to use the > > "lumped" L2 projection (e.g. ex13). If memory serves, that solution > > "looked" slightly better (at least in 2D). > > > >> Many people give up and just regularize the problem boundary > >> conditions. > > > > Indeed, the hyperbolic tangenttype regularized boundary conditions > > seem to be > > fairly standard in the literature for this type of problem. If we > > just > > want to be sure Stokes+AMR+Tets is working, let's try a test problem > > with continuous data? > > > > J 