Strange behavior on the overlapping region

General Discussion
1

I am trying to solve a 2D lid-driven cavity in parallel to test numerical schemes. The result sometimes looks strange in the overlapping region. For instance, the code diverges quickly running with -n 4, but shows a plausible result with non-overlapping mesh(-n 0).

snapshot: run with ff-mpirun -n 4
snapshot: run with ff-mpirun -n 4911×904 7.12 KB

Such discrepancies always lead to a divergence.
I am not sure the reason. suggestions would be appreciated.
Best regards.

2

Such things can happen easily by improperly handling the overlapping parts. However, without the code, it is impossible to help.

3

See, e.g., the role of the function exchange() in FreeFem-tutorial - Section 8 - example2.edp and the named parameter exchange in the function ChangeNumbering() described slide 50 of https://joliv.et/FreeFem-tutorial/main.pdf

4

Thank you for all your helpful comments.
I put part of my code below because the whole code is too long:

    /* u1[]=Au1^-1*rhsu1;
    u2[]=Au2^-1*rhsu2; */
    ChangeNumbering(Au1,rhsu1,u1PETSc);
    ChangeNumbering(Au2,rhsu2,u2PETSc);
    KSPSolve(Au1,u1PETSc,u1xPETSc);
    KSPSolve(Au2,u2PETSc,u2xPETSc);
    ChangeNumbering(Au1,u1[],u1xPETSc, inverse = true, exchange = true);
    ChangeNumbering(Au2,u2[],u2xPETSc, inverse = true, exchange = true);

    UpdateVecDk(u)
    real[int] rhsp=PRHS(0,Mh,tgv=-1);
    /* phi[]=Ap^-1*rhsp; */
    
    ChangeNumbering(Ap,rhsp,pPETSc);
    KSPSolve(Ap,pPETSc,pxPETSc);
    ChangeNumbering(Ap,phi[],pxPETSc, inverse = true, exchange = true);

    dxu1=nu*dx(u1p);
    dyu2=nu*dy(u2p);
    //update p by p=\phi+2p^{n}-p^{n-1}-\nu div(1.5u^{n+1}-2u^{n}+0.5u{n-1})
    p[]=phi[];
    p[]+=pe[];
    p[]-=dxu1[];
    p[]-=dyu2[];

The complete code is attached also:
Cavity2D.edp (6.2 KB)

I think the exchange=true argument should make the solution consistent, but the issue remains.

5

The derivatives won’t be consistent, so you need to exchange those values.

6

You are right. It is essential to ensure every involved variable to be consistent.
Now these derivatives are exchanged:

    dxu1=nu*dx(u1p);
    dyu2=nu*dy(u2p);
    exchange(Ap,dxu1[]);
    exchange(Ap,dyu2[]);

Thanks for your insight.