[petsc-users] Hessenberg Index-2 DAE and IMEX

Tang, Qi tangqi at msu.edu
Tue Feb 15 10:27:38 CST 2022

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.


On Feb 15, 2022, at 8:51 AM, Zhang, Hong <hongzhang at anl.gov<mailto:hongzhang at anl.gov>> 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 <tangqi at msu.edu<mailto:tangqi at msu.edu>> wrote:


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?
If we do not have to, do we expect to get high order in time?


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