Step 20: Run an experiment with Shells

Now, run Shells again, for an actual dynamical simulation experiment! Check the table under Step 16, and be sure that all input and output files are linked to the job, either by providing file names at run time, or by assigning them in a batch file.

Shells should provide a table called "Iteration History" as part of its text output in the t______.out file (Fortran device 6), and it should look something like this:

ITERATION HISTORY:
                                                               RELATIVE
                                          CORRE-     MAXIMUM       MEAN
                                 RELATIVE LATION  VERTICALLY VERTICALLY
                         MAXIMUM     MEAN   WITH  INTEGRATED INTEGRATED
 ITER-           RMS    VELOCITY VELOCITY   LAST      STRESS     STRESS
 ATION      VELOCITY      CHANGE   CHANGE CHANGE       ERR0R      ERR0R

     1  6.671025E-11  1.4950E-10 1.000000   ----  1.7092E+16    .993490
     2  6.304374E-11  4.0193E-11  .137291   -.63  3.6075E+13    .378274
     3  6.171746E-11  1.8318E-11  .066566    .76  4.7169E+13    .346676
     4  6.110019E-11  9.6699E-12  .054420    .94  4.3406E+13    .339420
     5  6.097313E-11  6.9601E-12  .042287    .99  3.5744E+13    .321039
     6  6.104579E-11  4.8806E-12  .030164    .99  3.5259E+13    .288665
     7  6.111884E-11  3.6560E-12  .021870    .99  3.2814E+13    .249889
     8  6.116438E-11  2.7920E-12  .016233   1.00  3.4038E+13    .210514
     9  6.120358E-11  2.2050E-12  .012962   1.00  1.8886E+13    .177277
    10  6.123600E-11  1.7543E-12  .010455   1.00  2.0459E+13    .151851
    11  6.124162E-11  1.3929E-12  .008227   1.00  2.8621E+13    .129272
    12  6.124802E-11  1.2190E-12  .006900   1.00  2.5601E+13    .111101
    13  6.124833E-11  1.1118E-12  .005794   1.00  1.8946E+13    .097004
    14  6.123912E-11  1.0577E-12  .005094   1.00  1.2855E+13    .085483
    15  6.123926E-11  9.6767E-13  .004568   1.00  1.0113E+13    .074999
    16  6.123978E-11  8.6750E-13  .003997   1.00  8.9478E+12    .064639
    17  6.124278E-11  7.5090E-13  .003491   1.00  9.2755E+12    .057505
    18  6.125361E-11  6.4242E-13  .003049   1.00  7.3854E+12    .050013
    19  6.127198E-11  5.5315E-13  .002617   1.00  6.6525E+12    .044480
    20  6.129393E-11  4.7318E-13  .002212   1.00  5.3433E+12    .039265
    21  6.131728E-11  4.0393E-13  .001880   1.00  6.8598E+12    .034951
    22  6.134085E-11  3.4605E-13  .001606   1.00  8.2828E+12    .031143
    23  6.136439E-11  2.9741E-13  .001391   1.00  7.3014E+12    .027845
    24  6.138654E-11  2.5652E-13  .001205   1.00  6.0201E+12    .025084
    25  6.140663E-11  2.2168E-13  .001046   1.00  5.5352E+12    .022969
    26  6.142430E-11  1.9390E-13  .000916   1.00  5.1053E+12    .021258
    27  6.143915E-11  1.7637E-13  .000805   1.00  4.6690E+12    .019945
    28  6.145105E-11  1.8290E-13  .000706   1.00  4.1747E+12    .018810
    29  6.146025E-11  1.9527E-13  .000624   1.00  4.8535E+12    .017693
    30  6.146818E-11  2.0409E-13  .000568   1.00  6.0509E+12    .016545
    31  6.147545E-11  2.0975E-13  .000523   1.00  4.0108E+12    .014991
    32  6.148303E-11  2.1244E-13  .000495   1.00  3.9696E+12    .013836
    33  6.149065E-11  2.1109E-13  .000467   1.00  3.8282E+12    .012943
    34  6.149793E-11  2.0582E-13  .000437   1.00  3.6485E+12    .012218
    35  6.150450E-11  1.9935E-13  .000399   1.00  4.1463E+12    .011425
    36  6.151064E-11  1.9136E-13  .000369   1.00  4.7319E+12    .010748
    37  6.151652E-11  1.8137E-13  .000342   1.00  3.3119E+12    .009961
    38  6.152232E-11  1.7012E-13  .000318   1.00  3.9367E+12    .009267
    39  6.152796E-11  1.5838E-13  .000295   1.00  3.9631E+12    .008742
    40  6.153339E-11  1.4642E-13  .000274   1.00  1.9996E+12    .008194
    41  6.153864E-11  1.3427E-13  .000257   1.00  1.8821E+12    .007794
    42  6.154367E-11  1.2248E-13  .000242   1.00  1.8185E+12    .007416
    43  6.154861E-11  1.1111E-13  .000229   1.00  1.9659E+12    .007063
    44  6.155340E-11  1.0026E-13  .000218   1.00  1.7831E+12    .006717
    45  6.155805E-11  9.0069E-14  .000207   1.00  1.5092E+12    .006341
    46  6.156260E-11  8.0702E-14  .000197   1.00  1.4318E+12    .006023
    47  6.156717E-11  7.2161E-14  .000189   1.00  1.3508E+12    .005732
    48  6.157177E-11  6.4406E-14  .000180   1.00  1.3697E+12    .005473
    49  6.157626E-11  5.7332E-14  .000173   1.00  1.6307E+12    .005227
    50  6.158074E-11  5.0900E-14  .000165   1.00
 ITERATION LIMIT REACHED BEFORE CONVERGENCE.
 ----------------------------------------------------------------------

All units are SI, so the "RMS velocity" and "Maximum velocity change" are in m/s (typically a very small number), and the "Maximum vertically-integrated stress error" is in Pa m, or N/m (a very large number).

If we graph the two dimensionless measures of this table using a logarithmic scale, we should see steady progress:

If you do not get steady convergence, the most likely causes are:

 The solution to the problem you have posed includes one or more "landslides" (localized flows down a topographic gradient) with very high steady-state velocities. The symptom of this is that the RMS velocity (column 2 in the table above) increases in each iteration, in a pattern of quasi-exponential growth. The solution to such cases is to plot the velocity solution (even though it is not converged) to see where the landslide(s) is/are. Then, you can strengthen the lithosphere either locally (by moderating the heat-flow or topography) or globally (by changing rheologic constants).

 If there is steady convergence at first, and then a transition to a limiting "noise level" of velocity change and/or stress error, then actually this is normal. (It is just that we usually stop the program before this level is reached.) The "noise level" is largely determined by input parameter OKDELV, which is a velocity (in m/s) precision that we hope to reach, but may not. If this parameter is too large, then convergence will be rapid, but the solution will not be accurate. (This is because the maximum limit on viscosity will be set rather low, and thus the viscosity limit rather than the desired flow law will determine the strain rate at many points.) However, if this parameter is made very small, later iterations may be "wasted" in the sense that the computer runs on but the solution no longer improves.