---------------------------------------------------------------------------------------------------- python: fvm : example 3:1d momentum equation, 1d continuity equation,pipeflow,tabulate,version 1.0 peter.vlasschaert@gmail.com,09/02/2023 ---------------------------------------------------------------------------------------------------- see : https://www.youtube.com/watch?v=N85HmIIgm4s&t=1333s , my website:maxima code ---------------------------------------------------------------------------------------------------- output :values from cvg ------------------------------- -> output array from nupy ------------------------------- [[ 0.00000000e+00 1.92600000e+01 5.77800000e+01 2.67200000e+00 -1.42108547e-14 1.66000000e+01 2.18586387e-01] [ 1.00000000e+00 5.14527418e+00 1.54358226e+01 -1.04484864e+00 0.00000000e+00 5.85863951e-01 5.32013472e-02] [ 2.00000000e+00 2.79521058e+00 8.38563175e+00 1.02739700e+01 0.00000000e+00 4.22054106e-01 7.60537476e-01] [ 3.00000000e+00 2.71216485e+00 8.13649456e+00 1.68038840e+01 0.00000000e+00 5.66082252e-01 8.09125283e-01] [ 4.00000000e+00 2.29112258e+00 6.87336774e+00 2.01752107e+01 -8.88178420e-16 3.52119205e-01 5.79013027e-01] [ 5.00000000e+00 2.20161583e+00 6.60484749e+00 2.19876173e+01 0.00000000e+00 2.41900106e-01 4.15998126e-01] [ 6.00000000e+00 2.08776720e+00 6.26330161e+00 2.29339111e+01 -8.88178420e-16 1.45665668e-01 2.56589377e-01] [ 7.00000000e+00 2.05658202e+00 6.16974606e+00 2.34386799e+01 0.00000000e+00 8.16846477e-02 1.53269288e-01] [ 8.00000000e+00 2.02505748e+00 6.07517243e+00 2.37028921e+01 0.00000000e+00 4.62442155e-02 8.51125859e-02] [ 9.00000000e+00 2.01577363e+00 6.04732088e+00 2.38435324e+01 -8.88178420e-16 2.42389142e-02 4.69530928e-02] [ 1.00000000e+01 2.00704626e+00 6.02113878e+00 2.39172059e+01 8.88178420e-16 1.33863532e-02 2.50384698e-02] [ 1.10000000e+01 2.00438762e+00 6.01316286e+00 2.39563927e+01 8.88178420e-16 6.88275980e-03 1.34562759e-02] [ 1.20000000e+01 2.00197300e+00 6.00591899e+00 2.39769286e+01 0.00000000e+00 3.76908294e-03 7.08774912e-03] [ 1.30000000e+01 2.00121974e+00 6.00365922e+00 2.39878473e+01 0.00000000e+00 1.92907772e-03 3.77945333e-03] [ 1.40000000e+01 2.00055175e+00 6.00165526e+00 2.39935710e+01 0.00000000e+00 1.05291526e-03 1.98404164e-03] [ 1.50000000e+01 2.00033905e+00 6.00101714e+00 2.39966133e+01 0.00000000e+00 5.38669773e-04 1.05544225e-03] [ 1.60000000e+01 2.00015423e+00 6.00046270e+00 2.39982085e+01 -8.88178420e-16 2.93495615e-04 5.53633395e-04] [ 1.70000000e+01 2.00009425e+00 6.00028274e+00 2.39990562e+01 8.88178420e-16 1.50257378e-04 2.94265958e-04] [ 1.80000000e+01 2.00004310e+00 6.00012931e+00 2.39995008e+01 0.00000000e+00 8.17620057e-05 1.54350931e-04] [ 1.90000000e+01 2.00002620e+00 6.00007860e+00 2.39997370e+01 0.00000000e+00 4.18999902e-05 8.20070914e-05] [ 2.00000000e+01 2.00001204e+00 6.00003613e+00 2.39998609e+01 0.00000000e+00 2.27738075e-05 4.30217119e-05] [ 2.10000000e+01 2.00000728e+00 6.00002185e+00 2.39999267e+01 0.00000000e+00 1.16828284e-05 2.28512486e-05] [ 2.20000000e+01 2.00000337e+00 6.00001010e+00 2.39999612e+01 0.00000000e+00 6.34318378e-06 1.19904252e-05] [ 2.30000000e+01 2.00000203e+00 6.00000608e+00 2.39999796e+01 8.88178420e-16 3.25734465e-06 6.36729516e-06] [ 2.40000000e+01 2.00000094e+00 6.00000282e+00 2.39999892e+01 0.00000000e+00 1.76677449e-06 3.34173064e-06] [ 2.50000000e+01 2.00000056e+00 6.00000169e+00 2.39999943e+01 0.00000000e+00 9.08172729e-07 1.77417921e-06] [ 2.60000000e+01 2.00000026e+00 6.00000079e+00 2.39999970e+01 0.00000000e+00 4.92108650e-07 9.31331508e-07] [ 2.70000000e+01 2.00000016e+00 6.00000047e+00 2.39999984e+01 -1.77635684e-15 2.53200472e-07 4.94356730e-07]] -> first row of numpy array ------------------------------- [ 0.00000000e+00 1.92600000e+01 5.77800000e+01 2.67200000e+00 -1.42108547e-14 1.66000000e+01 2.18586387e-01] -> output table with tabulate ------------------------------- Iteration uA uB P2 b u_residual c_residual ----------- -------- -------- -------- ------------ ------------ ------------ 0 19.26 57.78 2.672 -1.42109e-14 16.6 0.218586 1 5.14527 15.4358 -1.04485 0 0.585864 0.0532013 2 2.79521 8.38563 10.274 0 0.422054 0.760537 3 2.71216 8.13649 16.8039 0 0.566082 0.809125 4 2.29112 6.87337 20.1752 -8.88178e-16 0.352119 0.579013 5 2.20162 6.60485 21.9876 0 0.2419 0.415998 6 2.08777 6.2633 22.9339 -8.88178e-16 0.145666 0.256589 7 2.05658 6.16975 23.4387 0 0.0816846 0.153269 8 2.02506 6.07517 23.7029 0 0.0462442 0.0851126 9 2.01577 6.04732 23.8435 -8.88178e-16 0.0242389 0.0469531 10 2.00705 6.02114 23.9172 8.88178e-16 0.0133864 0.0250385 11 2.00439 6.01316 23.9564 8.88178e-16 0.00688276 0.0134563 12 2.00197 6.00592 23.9769 0 0.00376908 0.00708775 13 2.00122 6.00366 23.9878 0 0.00192908 0.00377945 14 2.00055 6.00166 23.9936 0 0.00105292 0.00198404 15 2.00034 6.00102 23.9966 0 0.00053867 0.00105544 16 2.00015 6.00046 23.9982 -8.88178e-16 0.000293496 0.000553633 17 2.00009 6.00028 23.9991 8.88178e-16 0.000150257 0.000294266 18 2.00004 6.00013 23.9995 0 8.1762e-05 0.000154351 19 2.00003 6.00008 23.9997 0 4.19e-05 8.20071e-05 20 2.00001 6.00004 23.9999 0 2.27738e-05 4.30217e-05 21 2.00001 6.00002 23.9999 0 1.16828e-05 2.28512e-05 22 2 6.00001 24 0 6.34318e-06 1.19904e-05 23 2 6.00001 24 8.88178e-16 3.25734e-06 6.3673e-06 24 2 6 24 0 1.76677e-06 3.34173e-06 25 2 6 24 0 9.08173e-07 1.77418e-06 26 2 6 24 0 4.92109e-07 9.31332e-07 27 2 6 24 -1.77636e-15 2.532e-07 4.94357e-07 >>>