On Tue, Feb 15, 2022 at 1:39 PM Zhang, Hong via petsc-users < [email protected]> wrote:
> Yes. I am talking about a general usage. To be accurate, direct > application of these methods does not always work. There are examples of > high-index DAEs for which backward Euler and all multi-step and RK methods > fail. You can find one such example in > https://www.cs.usask.ca/~spiteri/M314/notes/AP/chap10.pdf > This note also mentions the difficulties in solving the nonlinear system > and calculating error estimate for index-2 DAEs. > > Thus we do not recommend solving index-2 DAEs directly with these methods. > I have an index-2 DAE (earthquake mechanics), and we had to explicitly differentiate the constraint and add terms back in the momentum equation. This is also what is done for Navier-Stokes (I think they call it a segregated timestepping method). Thanks, Matt > Hong > > On Feb 15, 2022, at 10:27 AM, Tang, Qi <[email protected]> wrote: > > Thanks a lot, Hong. > > I would think if one use BDF or backward Euler for incompressible Naiver > Stokes, it should work with the index 2 equation. Why do you think it will > not work? Or maybe you were talking about a general usage. > > INS is not my usage but I am still curious. We have some unconventional > constraint equation. > > Qi > > > > On Feb 15, 2022, at 8:51 AM, Zhang, Hong <[email protected]> wrote: > > Hi Qi, > > The index-2 DAE cannot be solved directly with ARK or implicit methods > such as backward Euler and Crank-Nicolson. You need to convert the system > to an index-1 DAE as illustrated in the documentation. > > Hong (Mr.) > > On Feb 15, 2022, at 9:43 AM, Tang, Qi <[email protected]> wrote: > > Hi, > > Does PETSc’s ARK directly apply to Hessenberg Index-2 DAE? Do we need to > perform a time derivative of the constraint equation by ourselves first? > https://petsc.org/main/docs/manual/ts/#hessenberg-index-2-dae > <https://urldefense.com/v3/__https://petsc.org/main/docs/manual/ts/*hessenberg-index-2-dae__;Iw!!HXCxUKc!kM_qeX09WwLuE991Vn6u85M0vDlNnqMA0Diuy84sqZawkGLr-MNDkYVisStQBA$> > If we do not have to, do we expect to get high order in time? > > Thanks, > Qi > > > > > > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
