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python: fvm : example 3:1d momentum equation, 1d continuity equation,pipeflow,version 1.0  
 peter.vlasschaert@gmail.com,09/02/2023                                                    
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 see : https://www.youtube.com/watch?v=N85HmIIgm4s&t=1333s , my website:maxima code        
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Solving
Iteration: 0
uA: 19.26
uB: 57.780000000000015
P2: 2.672
b: -1.4210854715202004e-14
u_residual: 16.6
c_residual: 0.2185863874345549
------------------------------
Iteration: 1
uA: 5.145274184839044
uB: 15.435822554517133
P2: -1.0448486399999992
b: 0.0
u_residual: 0.5858639513145972
c_residual: 0.05320134722827769
------------------------------
Iteration: 2
uA: 2.7952105832720235
uB: 8.38563174981607
P2: 10.273970035308631
b: 0.0
u_residual: 0.4220541060382525
c_residual: 0.7605374764061834
------------------------------
Iteration: 3
uA: 2.7121648527624656
uB: 8.136494558287396
P2: 16.803884045468813
b: 0.0
u_residual: 0.5660822518430005
c_residual: 0.8091252830088822
------------------------------
Iteration: 4
uA: 2.2911225797000254
uB: 6.873367739100077
P2: 20.17521065931208
b: -8.881784197001252e-16
u_residual: 0.3521192046178893
c_residual: 0.5790130266926747
------------------------------
Iteration: 5
uA: 2.201615828658505
uB: 6.604847485975514
P2: 21.98761727589457
b: 0.0
u_residual: 0.2419001059375852
c_residual: 0.41599812635291217
------------------------------
Iteration: 6
uA: 2.0877672039471533
uB: 6.26330161184146
P2: 22.933911122230665
b: -8.881784197001252e-16
u_residual: 0.14566566793973126
c_residual: 0.2565893772567426
------------------------------
Iteration: 7
uA: 2.0565820207768577
uB: 6.169746062330573
P2: 23.438679911499182
b: 0.0
u_residual: 0.08168464772244913
c_residual: 0.15326928800870773
------------------------------
Iteration: 8
uA: 2.0250574777699684
uB: 6.0751724333099055
P2: 23.70289206559177
b: 0.0
u_residual: 0.046244215477692134
c_residual: 0.08511258591937565
------------------------------
Iteration: 9
uA: 2.01577362603707
uB: 6.04732087811121
P2: 23.843532425818285
b: -8.881784197001252e-16
u_residual: 0.024238914221202102
c_residual: 0.046953092825452736
------------------------------
Iteration: 10
uA: 2.0070462591727023
uB: 6.0211387775181064
P2: 23.917205870741487
b: 8.881784197001252e-16
u_residual: 0.013386353198565367
c_residual: 0.02503846982370331
------------------------------
Iteration: 11
uA: 2.004387620202499
uB: 6.013162860607497
P2: 23.956392723252797
b: 8.881784197001252e-16
u_residual: 0.00688275979896672
c_residual: 0.013456275913516775
------------------------------
Iteration: 12
uA: 2.001972996755629
uB: 6.005918990266887
P2: 23.97692862495303
b: 0.0
u_residual: 0.0037690829398938225
c_residual: 0.007087749117070299
------------------------------
Iteration: 13
uA: 2.0012197410639003
uB: 6.0036592231917005
P2: 23.98784733999391
b: 0.0
u_residual: 0.0019290777153220407
c_residual: 0.0037794533282846216
------------------------------
Iteration: 14
uA: 2.000551753849231
uB: 6.001655261547692
P2: 23.993570984463155
b: 0.0
u_residual: 0.0010529152593303501
c_residual: 0.0019840416430334097
------------------------------
Iteration: 15
uA: 2.000339045766228
uB: 6.001017137298684
P2: 23.996613296538833
b: 0.0
u_residual: 0.0005386697731335501
c_residual: 0.0010554422463807248
------------------------------
Iteration: 16
uA: 2.0001542325741943
uB: 6.0004626977225834
P2: 23.998208507258493
b: -8.881784197001252e-16
u_residual: 0.0002934956147115489
c_residual: 0.0005536333946962118
------------------------------
Iteration: 17
uA: 2.0000942457675808
uB: 6.000282737302741
P2: 23.999056198291118
b: 8.881784197001252e-16
u_residual: 0.00015025737818113663
c_residual: 0.00029426595831514923
------------------------------
Iteration: 18
uA: 2.0000431041674003
uB: 6.000129312502201
P2: 23.999500786951337
b: 0.0
u_residual: 8.17620056501148e-05
c_residual: 0.00015435093144773913
------------------------------
Iteration: 19
uA: 2.0000261996180337
uB: 6.000078598854101
P2: 23.999736983306747
b: 0.0
u_residual: 4.189999020568009e-05
c_residual: 8.200709143578329e-05
------------------------------
Iteration: 20
uA: 2.0000120449223933
uB: 6.00003613476718
P2: 23.999860890338656
b: 0.0
u_residual: 2.2773807475604014e-05
c_residual: 4.302171191851639e-05
------------------------------
Iteration: 21
uA: 2.0000072838607257
uB: 6.0000218515821775
P2: 23.99992670317228
b: 0.0
u_residual: 1.1682828436471886e-05
c_residual: 2.2851248622974186e-05
------------------------------
Iteration: 22
uA: 2.0000033654239773
uB: 6.000010096271932
P2: 23.999961235946238
b: 0.0
u_residual: 6.343183776163459e-06
c_residual: 1.1990425159471553e-05
------------------------------
Iteration: 23
uA: 2.0000020251734734
uB: 6.000006075520419
P2: 23.99997957385243
b: 8.881784197001252e-16
u_residual: 3.257344650263073e-06
c_residual: 6.367295160224192e-06
------------------------------
Iteration: 24
uA: 2.000000940222293
uB: 6.000002820666879
P2: 23.999989198063805
b: 0.0
u_residual: 1.7667744929877192e-06
c_residual: 3.341730639443432e-06
------------------------------
Iteration: 25
uA: 2.000000563113684
uB: 6.000001689341053
P2: 23.999994307707393
b: 0.0
u_residual: 9.081727285856384e-07
c_residual: 1.774179208410793e-06
------------------------------
Iteration: 26
uA: 2.0000002626507585
uB: 6.000000787952276
P2: 23.999996989944243
b: 0.0
u_residual: 4.921086495028065e-07
c_residual: 9.313315082053587e-07
------------------------------
The converged solution is the following:
Variable           Value
----------  ------------
Iteration   27
uA           2
uB           6
P2          24
b           -1.77636e-15
u_residual   2.532e-07
c_residual   4.94357e-07