Error when running Lid Driven Cavity demo

[TheCrowned]

Hello! This looks like a very interesting project. I am also working on the Navier-Stokes equations with FEniCS :)

I cloned the repo and tried to run the lid driven cavity demo as it is, but it does not seem to converge. Am I doing something wrong?

(fenics_env) stefano@r11e:~/git/VarMINT$ python demos/regularizedLDC.py 
Calling FFC just-in-time (JIT) compiler, this may take some time.
No Jacobian form specified for nonlinear variational problem.
Differentiating residual form F to obtain Jacobian J = F'.
Calling FFC just-in-time (JIT) compiler, this may take some time.
Calling FFC just-in-time (JIT) compiler, this may take some time.
Solving nonlinear variational problem.
  Newton iteration 0: r (abs) = 5.077e+01 (tol = 1.000e-10) r (rel) = 1.000e+00 (tol = 1.000e-09)
  Newton iteration 1: r (abs) = 4.238e-02 (tol = 1.000e-10) r (rel) = 8.346e-04 (tol = 1.000e-09)
  Newton iteration 2: r (abs) = 5.532e-03 (tol = 1.000e-10) r (rel) = 1.089e-04 (tol = 1.000e-09)
  Newton iteration 3: r (abs) = 4.750e-05 (tol = 1.000e-10) r (rel) = 9.355e-07 (tol = 1.000e-09)
  Newton iteration 4: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 5: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 6: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 7: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 8: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 9: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 10: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 11: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 12: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 13: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 14: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 15: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 16: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 17: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 18: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 19: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 20: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 21: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 22: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 23: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 24: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 25: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 26: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 27: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 28: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 29: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 30: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 31: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 32: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 33: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 34: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 35: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 36: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 37: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 38: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 39: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 40: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 41: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 42: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 43: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 44: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 45: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 46: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 47: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 48: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 49: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
  Newton iteration 50: r (abs) = -nan (tol = 1.000e-10) r (rel) = -nan (tol = 1.000e-09)
Traceback (most recent call last):
  File "demos/regularizedLDC.py", line 96, in <module>
    solve(F==0,up)
  File "/home/stot2794/anaconda3/envs/fenics_env/lib/python3.8/site-packages/dolfin/fem/solving.py", line 220, in solve
    _solve_varproblem(*args, **kwargs)
  File "/home/stot2794/anaconda3/envs/fenics_env/lib/python3.8/site-packages/dolfin/fem/solving.py", line 266, in _solve_varproblem
    solver.solve()
RuntimeError: 

*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
***     fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error:   Unable to solve nonlinear system with NewtonSolver.
*** Reason:  Newton solver did not converge because maximum number of iterations reached.
*** Where:   This error was encountered inside NewtonSolver.cpp.
*** Process: 0
*** 
*** DOLFIN version: 2019.1.0
*** Git changeset:  c5b9b269f4a6455a739109e3a66e036b5b8412f5
*** -------------------------------------------------------------------------

[david-kamensky]

I'm not able to reproduce this using my personal setup, which is FEniCS 2019.2.0.dev0, installed on Ubuntu, through the package manager. The residuals from the first four steps are identical, but then it continues to converge for another step, meets the convergence criterion, and prints out the error. It's likely not an issue with changes to the FEniCS software itself, since I would have originally written this with an older version (also installed on Ubuntu). The only thing I can think of is some difference in the versions of third-party libraries.

One potential issue I can think of is that the problem is technically ill-posed, because there is no mechanism to pin down the hydrostatic mode in the pressure. You might try something like

# Pin pressure at one node to remove hydrostatic mode:
bc = DirichletBC(V.sub(1),Constant(0),"x[0]<DOLFIN_EPS && x[1]<DOLFIN_EPS",
                 "pointwise")

# Solve for velocity and pressure:
solve(F==0,up,bcs=[bc,])

This produces an essentially-identical velocity solution for me (and remains consistent with the arbitrarily-selected pressure p_exact).

[TheCrowned]

Thanks, that tweak made it work! I am running fenics 2019.1.0 on Ubuntu.

Invoked with python demos/regularizedLDC.py --viz --Re 100 --Nel 100, is this the velocity plot I am supposed to get?

[david-kamensky]

is this the velocity plot I am supposed to get?

This looks qualitatively correct. You can get a quantitative convergence check from the error measures printed at the end of the script. Note that this differs from the classic lid-driven cavity problem, in that it is "regularized" to have a known smooth exact solution (thus enabling the quantitative convergence check).

I went ahead and pushed the changes to the repository, so hopefully nobody will run into this issue in the future.