I used svOneDSolver to perform a basic one-dimensional simulation of a steady-state problem in a straight tube. I input a flow rate of 100 ml/s and ran it for 100 steps with a time step of 0.001s . In theory, a steady-state problem should reach the ideal result in just a few steps. However, the results showed that the flow rate gradually increased along the length of the tube. Even at 0.1s, the flow rate at the last point was only around 52 ml/s (Under the condition that the area of the tube remains nearly constant). This seems completely different from the three-dimensional problem. In the three-dimensional problem, even if the blood vessels are deformable, the flow rates at the inlet and outlet would not differ so significantly.
Is it because, in the one-dimensional assumption, there is no fluid in the vessel before the simulation, and the fluid enters slowly during the simulation? On the other hand, in the three-dimensional simulation, it is assumed that the vessel is already filled with fluid before the simulation, so when a flow rate of 100 ml/s is applied at the inlet, the fluid exits at almost the same flow rate due to the incompressibility of the fluid.
Here are the files (test.in) and results (test_seg0_flow.dat) from my simulation. Why is there such a significant difference in the flow rate in the one-dimensional simulation? Could it be as I suspected?
Any help will be appreciated.
Lina
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# ================================
# MODEL - UNITS IN CGS
# ================================
MODEL test_
NODE 0 0 0 0
NODE 1 15 0 0
SEGMENT seg0 0 15 30 0 1 10 10 100.0 MAT1 NONE 0.0 0 0 RESISTANCE RESISTANCE_1
DATATABLE RESISTANCE_1 LIST
0.0 500
0.0 0.0
ENDDATATABLE
DATATABLE INFLOW LIST
0.0 100
1.0 100
ENDDATATABLE
SOLVEROPTIONS 0.001 1 100 2 INFLOW FLOW 1.0e-8 1 1
MATERIAL MAT1 OLUFSEN 1.06 0.04 0.0 1.0 20000000.0 -22.5267 865000.0
OUTPUT TEXT
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100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0 62.1220850263 92.133425183 98.6218783348 99.7734945915 99.9604650742 99.9897685215 99.994559175 99.9955828963 99.9959765225 99.9962226422 99.9964072507 99.9965535785 99.9966724542 99.99677062 99.9968526491 99.996921424 99.9969776236 99.9970171494 99.9970234006 99.996947157 99.9966589712 99.9958458992 99.9938061333 99.9890758173 99.9788135312 99.9578900232 99.9177093468 99.8449411033 99.7205628834 99.5198395931 99.2139896635 98.7741641742 98.1778807028 97.4172087316 96.5069791008 95.490459603 94.4397771429 93.4492477046 92.6217090313 92.0504052444 91.800961112 91.8985007139 92.3235796285 93.017800933 93.8969730703 94.8676864483 95.8428691044 96.7530348774 97.5518112496 98.2161087251 98.7424411753 99.141293031 99.4312131351 99.6337766118 99.7699571949 99.8579654905 99.9123052469 99.9436744354 99.9593433409 99.9637197043 99.9589122901 99.9451976352 99.9213657802 99.8849671047 99.8325077295 99.7596505684 99.6614772064 99.5328547699 99.3689329316 99.1657699933 98.9210552686 98.6348610653 98.3103266947 97.9541559764 97.5768060005 97.1922645059 96.8173586133 96.4706056348 96.1706973384 95.9347864552 95.776799693 95.706018788 95.72614172 95.8349633916 96.024713761 96.2829843548 96.5940849779 96.940619141 97.3050566458 97.6711112419 98.02478818 98.3550351102 98.6539951957 98.9169128873 99.1417751926 99.3287842036 99.4797533586 99.5975054733 99.6853303839 99.7465387169
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0 10.1449866819 41.9842879373 75.8821571304 92.7482251587 98.1987614372 99.5967788907 99.9086404154 99.9725485725 99.9853229635 99.9881770765 99.9891164363 99.9896334007 99.9900118257 99.9903159383 99.9905674475 99.990776051 99.9909415655 99.99104342 99.9910086345 99.9906314841 99.9893906665 99.9860681741 99.9780218964 99.9599198434 99.9217481415 99.8460186521 99.7043880742 99.4543820004 99.0375228703 98.380682423 97.4025871961 96.0267477699 94.200465734 91.9171671666 89.2367754639 86.297238295 83.3107899998 80.5416657471 78.2673044969 76.7308666052 76.0967627892 76.4209414849 77.6435877152 79.6051961782 82.0803514 84.8194054223 87.5876990404 90.1945540819 92.5084500045 94.458888636 96.0282647956 97.2381970438 98.1344797925 98.7736720549 99.2129379915 99.5035340008 99.6875102937 99.796789431 99.8537146883 99.872300048 99.8596427297 99.8171939695 99.7417779196 99.6263858329 99.4608549629 99.2325778212 98.9273868881 98.5307293052 98.0291901112 97.4123457518 96.6748388834 95.8184721382 94.8540384653 93.8025581478 92.6955966642 91.5744069618 90.4877769621 89.4886550178 88.6298419965 87.9592351167 87.5152381896 87.322977849 87.3918700724 87.7148794668 88.2695463879 89.0205814186 89.9236007639 90.9294421566 91.9884760908 93.0544023938 94.0871679076 95.054818606 95.9342714845 96.71113022 97.3787589913 97.9368687324 98.3898665885 98.7451848561 99.0117540699 99.1987284707
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0 0.66093825677 5.35836141341 19.5936170232 43.6141770623 68.705576514 86.1681902433 94.9422437536 98.3978373431 99.5365455933 99.8654285542 99.9517268961 99.9731220674 99.9785237954 99.9801710995 99.9809180269 99.9813914575 99.9816901114 99.9817108073 99.9810824653 99.9788486696 99.9727828048 99.9580965791 99.9252371781 99.856505696 99.7214597776 99.4715653521 99.0353302524 98.3160203502 97.1946696016 95.5409685468 93.2333343622 90.1869417556 86.3852026806 81.9072068398 76.9423834643 71.7852345035 66.8075207414 62.4114746225 58.9732058778 56.7883082277 56.0308452582 56.7330604103 58.7879951409 61.9724001407 65.9839220569 70.4848660373 75.1447800186 79.6754203349 83.8539592736 87.5330484268 90.6389259541 93.1606007056 95.1339729231 96.6245985624 97.7119614648 98.4769727536 98.9933141945 99.3224020996 99.5112534618 99.5923623841 99.5847587885 99.4956216504 99.3220659222 99.0529510516 98.6707314588 98.1534691274 97.4771540438 96.6184370886 95.5577854675 94.2829409811 92.79241939 91.0986623265 89.2303714425 87.2335453296 85.1708216807 83.1189029067 81.1640947443 79.3962753267 77.9018832028 76.7567107032 76.0193689195 75.7262311668 75.8884707292 76.4915209544 77.4969542782 78.8464601551 80.4673519156 82.2788845595 84.1986333818 86.1482594358 88.0581469042 89.8706035633 91.5415303442 93.0406561752 94.3505767725 95.4649203245 96.3859902184 97.1222149495 97.685682779 98.0899690743
0 0.265023876538 2.50427157 10.7668788083 28.2976220089 52.0514465269 73.9024509126 88.3221678293 95.5751293751 98.5271234317 99.5483827751 99.860203144 99.9468678081 99.9695666505 99.9755430002 99.9773671348 99.9781267584 99.978472965 99.9783362201 99.9771224178 99.9732958981 99.9633821463 99.9401406222 99.8895901106 99.7866937513 99.589902698 99.2354564952 98.6332492044 97.666896028 96.2009003564 94.0970247038 91.2398489468 87.5683142266 83.1067187963 77.9865587463 72.4511311509 66.8384341226 61.5436977713 56.9687203604 53.4687132765 51.3073136893 50.6272815329 51.4399047489 53.632139731 56.9879921194 61.2195395708 66.0027291161 71.0131729482 75.9575435859 80.5970139709 84.7606054859 88.3481110014 91.3240195958 93.7051295164 95.5450346947 96.9184229303 97.9073602504 98.5907691044 99.0374129336 99.3020465151 99.4240370356 99.4276742161 99.3234907499 99.1101161838 98.7764092199 98.3037989932 97.668883352 96.846370401 95.8124129146 94.5482891114 93.0442511578 91.3032239912 89.3439242922 87.2029146179 84.935135934 82.6125847025 80.3210103728 78.1547766257 76.2103086018 74.578784837 73.3388783688 72.5503763439 72.2494060668 72.4457877183 73.1227582283 74.2390139037 75.7327470436 77.5271407219 79.5366601455 81.6734478281 83.8531883717 85.999939664 88.0496047566 89.9519123742 91.6709549998 93.1844791507 94.4822191311 95.5636099936 96.4352128378 97.1081471171 97.595763917
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0 0.0427533671918 0.517232461205 2.89516385451 10.0203140179 24.2615845878 44.3606705399 65.1598851711 81.4838718642 91.5558996045 96.6284468235 98.7891263255 99.5918095251 99.8586610817 99.9399172021 99.9631823661 99.9696431671 99.9711914068 99.9704593288 99.9666099958 99.9559991107 99.9305616014 99.8745180475 99.7594642902 99.5381937879 99.1383908682 98.4583726428 97.3679255904 95.7173860424 93.3568932849 90.1650177925 86.0822510889 81.1414307381 75.485775134 69.3671331915 63.1222913663 57.1319403543 51.7722891744 47.3708767971 44.1753449048 42.3384762335 41.9174367858 42.8821127339 45.1273626122 48.4860452742 52.742233297 57.6456655079 62.9285945134 68.324996214 73.5904696099 78.5199998149 82.9606571149 86.8172683183 90.0506671325 92.6696820018 94.7190583514 96.2658360777 97.3863958833 98.1557011842 98.6394773208 98.8894025701 98.9409467316 98.8132973096 98.5108097716 98.0255274387 97.3404589884 96.4334166301 95.2812714138 93.8644660862 92.1715547757 90.2034424183 87.9769127817 85.5269988629 82.9077906484 80.1914026196 77.4650254552 74.8262302144 72.3769324773 70.2166101859 68.4354660753 67.1082189919 66.2891078124 66.0085252125 66.2715022613 67.058071316 68.32536613 70.0111847041 72.0386440239 74.3214950757 76.7696408707 79.2944109665 81.8131943379 84.253116564 86.5535596918 88.6674507098 90.5613708804 92.2146468432 93.6176629738 94.7696765164 95.6764226426 96.3477713753
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