[petsc-users] Custom matrix coloring for finite difference Jacobian

[Eirik Jaccheri Høydalsvik]

Hi,

I have made a two-phase flow code which computes motion of two phases in one dimension, where the phases are allowed to intermix. This code relies on a finite difference Jacobian computed using the standard coloring I get from the DMDA object:

   da = PETSc.DMDA().create(
        dim=(N_vertical,),
        dof=3,
        stencil_width=1,
    )

I now want to add a variable for the interphase height L_z in addition to a velocity u_v, giving the velocity of the vapor flowing in to the interface. The interface will move throughout the grid, meaning that these two variables will not be coupled to a fixed set of grid cells, but will be coupled to different sets of three grid cells throughout the simulation.

Questions:

1. Is it possible to create a custom coloring to efficiently compute the finite difference Jacobian including the interphase height and vapor velocity?

2. How do I revert to computing the full finite difference Jacobian with the purpose of testing if the interphase model works?

Best regards,
Eirik Jaccheri Høydalsvik
Sintef ER and NTNU EPT

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