Roy, I got an email saying that the attachments are awaiting moderator approval. That might explain why you did not get the attachment.
I'm solving a pure diffusion problem and there is no convection here. But I do understand that time integration makes a big difference and even making delt=1e-10 does not seem to help. The negativity occurs on the first step, the first call to nonlinear residual. When you say trapezoidal rule, are you talking about Implicit midpoint here because CN is based on the trapezoidal rule and is not L-stable (spurious oscillations are not damped). One other interesting thing that I just noticed is that if I make my initial solution bigger: originally it was uniformly 1e-5 and now I made it to 1e-0, the nonlinear iteration and time-stepping with CN proceeds correctly. So now I'm wondering whether nondimensionalization in some form could be the answer but with a diffusion coefficient as T^4, not sure if this will help much either. Thanks for the parallel comparisons though. Vijay On Tue, Jan 26, 2010 at 12:33 PM, Roy Stogner <[email protected]> wrote: > > On Tue, 26 Jan 2010, Vijay S. Mahadevan wrote: > >> The issue is that I get negative temperatures at the first element >> during assembly, immaterial of the refinement or the resolution of the >> domain. I do not understand this behavior and was wondering if there >> was a requirement with continuous FEM (Lagrange basis) that was not >> satisfied in these problems with non-smooth solutions. I am certain >> that there should be a fix to make sure that negative solutions are >> avoided and that energy was conserved. But all my literature search >> has not led to any decent solutions yet. > > Not sure about this particular problem (example wasn't attached, and I > wouldn't have time to read it if it was), but I've managed to avoid > similar "out-of-bounds solution" failures just by being careful about > the time discretization. For example the Galerkin H^2 formulation of > Cahn-Hilliard can blow up with Crank-Nicholson integration (where each > timestep can effectively extrapolate the solution out of the domain of > the equations) but works with trapezoidal integration (where the > residual terms at the end-of-timestep smoothly prevent that class of > error). > > Not sure what the best way to go is when you don't have that same > level of feedback in the residual, though. Oscillations in > convection-dominated transport can lead to negative concentrations, > which can then crash later physics despite being "reasonable" > solutions to the transport equations. > --- > Roy > ------------------------------------------------------------------------------ The Planet: dedicated and managed hosting, cloud storage, colocation Stay online with enterprise data centers and the best network in the business Choose flexible plans and management services without long-term contracts Personal 24x7 support from experience hosting pros just a phone call away. http://p.sf.net/sfu/theplanet-com _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
