Slow convergence in porous media flow

Description

The fluid equations were updated to add Brinkman porous media in #293 (see #236 and #292). The associated integration test test_driven_cavity_2d_porous takes 208s, 88s, and 68s on 1, 3, and 4 procs. This is long for a 2D test case. Looking at a recent pipeline, this is the output from test_driven_cavity_2d_porous[1]:

---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 NS 1-1  2.502e+01  [0 1.000e+00 1.000e+00 2.082e-08]  [2606 -4 97]
 NS 1-2  4.759e+01  [-29 3.250e-02 3.250e-02 6.397e-07]  [2339 -3 97]
 NS 1-3  6.582e+01  [-49 3.542e-03 3.542e-03 5.869e-06]  [1894 -7 96]
 NS 1-4  7.875e+01  [-69 3.332e-04 3.332e-04 6.251e-05]  [1325 -3 94]
 NS 1-5  8.926e+01  [-85 5.375e-05 5.375e-05 3.856e-04]  [1069 -5 93]
 NS 1-6  9.596e+01  [-98 1.245e-05 1.245e-05 1.669e-03]  [673 -12 88]
 NS 1-7  9.997e+01  [-109 3.256e-06 3.256e-06 6.390e-03]  [397 -7 80]
 NS 1-8  1.010e+02  [-121 8.760e-07 8.760e-07 2.371e-02]  [81 -37 26]
 NS 1-9  1.018e+02  [-132 2.379e-07 2.379e-07 8.671e-02]  [22 -24 4]
 NS 1-10  1.026e+02  [-143 6.767e-08 6.767e-08 3.041e-01]  [8 -12 1]
 NS 1-11  1.034e+02  [-151 2.728e-08 2.728e-08 7.570e-01]  [3 -3 0]
 NS 1-12  1.042e+02  [-153 2.136e-08 2.136e-08 9.660e-01]  [2 0 0]
 NS 1-13  1.050e+02  [-153 2.076e-08 2.076e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged
 NS 1-14  1.058e+02  [-153 2.053e-08 2.053e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged
 NS 1-15s 1.067e+02  [-153 2.046e-08 2.046e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged
 NS 2-1  1.339e+02  [0 1.000e+00 4.803e-01 4.320e-08]  [2767 0 97]
 NS 2-2  1.541e+02  [-30 2.862e-02 1.374e-02 1.511e-06]  [2097 -4 96]
 NS 2-3  1.702e+02  [-51 2.580e-03 1.239e-03 1.675e-05]  [1669 -10 95]
 NS 2-4  1.830e+02  [-69 3.202e-04 1.538e-04 1.351e-04]  [1259 0 94]
 NS 2-5  1.921e+02  [-84 5.638e-05 2.708e-05 7.678e-04]  [930 -10 91]
 NS 2-6  1.979e+02  [-98 1.232e-05 5.918e-06 3.511e-03]  [573 -4 86]
 NS 2-7  2.014e+02  [-110 3.135e-06 1.506e-06 1.383e-02]  [347 -4 78]
 NS 2-8  2.026e+02  [-121 8.277e-07 3.975e-07 5.236e-02]  [88 -29 29]
 NS 2-9  2.034e+02  [-132 2.256e-07 1.083e-07 1.918e-01]  [17 -17 2]
 NS 2-10  2.042e+02  [-142 7.382e-08 3.546e-08 5.862e-01]  [5 -5 1]
 NS 2-11  2.049e+02  [-146 4.639e-08 2.228e-08 9.274e-01]  [3 -1 0]
 NS 2-12  2.057e+02  [-147 4.340e-08 2.085e-08 9.872e-01]  [2 0 0]
 NS 2-13  2.065e+02  [-147 4.293e-08 2.062e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged
 NS 2-14  2.073e+02  [-147 4.264e-08 2.048e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged
 NS 2-15s 2.082e+02  [-147 4.248e-08 2.040e-08 1.000e+00]  !0 0 0!  WARNING: The linear system solution has not converged

The convergence is linear and extremely slow, and the residual stagnates around 1e-8. The linearization of the porous flow is likely not correct.

Reproduction

Run pytest -k porous.

Expected behavior

Always quadratic convergence

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines