On Tue, Dec 27, 2011 at 19:58, Feng-Chao Wang <wolfshow at gmail.com> wrote:
> ** > Dear all, > > I want to numerically solve a strongly nonlinear fourth-order equation > (2-D), which is used to describe the dynamics of a liquid film. > please find the form of the equation below or in the attachment, The > thickness of the film, H(X,Y,T) is the function to be solved, C, G, A0 are > constant parameters. > > > I wrote a PETSc programs for this problem, using CN method in time. > However, it does not work well. In some cases, there are some > negativevalues in the solution (Obviously, the thickness of the liquid film > could not be negative.) While in some other cases, the solution remains as > the initial condition, looking like the governing equation doesn't work at > all. > 1. Make sure that the equations are actually being solved, for instance with -snes_monitor -snes_converged_reason -ksp_converged_reason. 2. Start with a time integration method that has a discrete maximum principle. Implicit Euler has this property for many classes of systems, but CN does not. 3. Consider writing the system as a variational inequality if positivity is still a problem with the time steps you want to take. Then use SNESVIRS (or SNESVIRSAUG or SNESVISS). > > I think it is because that the solution of this equation may form infinite > fradient when the equation is developed. > > Some literatures reported that the similar problem was solved successfully > using the ADI (Alternating Direction Implicit) method. Unfortunately, I > found that the current PETSc doesn't support ADI. > > I also read a paper in which the similar equation was solved by using the > CN scheme in time. Besides, the author employed the modified second-order > upwind difference method to handle the nonlinear terms due to the inability > of the centered differences in space. > > I prefer to use PETSc because this powerful toolkit enables easy parallel > computation of PDE since I am not familar with MPI. Could anyone please > give me some suggestions on how I can solve the above equation within the > framework of PETSc? > > Thanks very much in advance! > > Feng-Chao Wang > > 2011-12-28 > ------------------------------ > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20111227/dfa209f6/attachment-0001.htm> -------------- next part -------------- A non-text attachment was scrubbed... Name: not available Type: image/jpeg Size: 52349 bytes Desc: not available URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20111227/dfa209f6/attachment-0001.jpeg>
