=================================================== ===== QUASI STEADY WAVE PROPARGATION ANALYSIS ===== =========== BY BOUNDARY ELEMENT METHOD ============ ============== USING LINEAR ELEMENT =============== == ALONG WITH STRAIGHT FORMATION OF [A]{X}={RHS} == =================================================== OMEGA = 6.28318500000000 ==== ELEMENT INFORMATION ==== ELEMENT # NODE(1) NODE(2) B.C. B-V(1)REAL B-V(1)IMAG B-V(2)REAL B-V(2)IMAG ----------------------------------------------------------------------------------------------- 1 1 2 NUEMANN 5.946890 1.932263 6.105510 1.349776 2 2 3 NUEMANN 5.870878 1.297905 5.998548 -0.4113262 3 3 4 NUEMANN 5.528293 -0.3790803 4.772719 -2.815470 4 4 5 NUEMANN 4.183325 -2.467781 1.948115 -4.449157 5 5 6 NUEMANN 1.598776 -3.651328 -1.363020 -3.745725 6 6 7 NUEMANN -1.012815 -2.783323 -2.779467 -1.023351 7 7 8 NUEMANN -1.711589 -0.6301774 -1.515396 1.015006 8 8 9 NUEMANN -0.5116851 0.3427246 0.1353149E-06 0.6158586 9 9 10 NUEMANN -0.1353154E-06 -0.6158609 -0.5116872 -0.3427257 10 10 11 NUEMANN -1.515394 -1.015004 -1.711587 0.6301776 11 11 12 NUEMANN -2.779469 1.023354 -1.012813 2.783327 12 12 13 NUEMANN -1.363017 3.745726 1.598776 3.651328 13 13 14 NUEMANN 1.948114 4.449156 4.183324 2.467781 14 14 15 NUEMANN 4.772719 2.815470 5.528293 0.3790777 15 15 16 NUEMANN 5.998549 0.4113234 5.870878 -1.297908 16 16 17 NUEMANN 6.105509 -1.349779 5.946890 -1.932263 17 17 18 NUEMANN 5.946890 -1.932263 6.105510 -1.349776 18 18 19 NUEMANN 5.870878 -1.297905 5.998548 0.4113261 19 19 20 NUEMANN 5.528293 0.3790803 4.772718 2.815473 20 20 21 NUEMANN 4.183323 2.467783 1.948111 4.449158 21 21 22 NUEMANN 1.598774 3.651330 -1.363024 3.745724 22 22 23 NUEMANN -1.012817 2.783321 -2.779467 1.023347 23 23 24 NUEMANN -1.711588 0.6301740 -1.515395 -1.015003 24 24 25 NUEMANN -0.5116871 -0.3427253 0.3691530E-07 -0.6158606 25 25 26 NUEMANN -0.3691530E-07 0.6158606 -0.5116872 0.3427252 26 26 27 NUEMANN -1.515397 1.015005 -1.711589 -0.6301790 27 27 28 NUEMANN -2.779467 -1.023354 -1.012812 -2.783326 28 28 29 NUEMANN -1.363017 -3.745729 1.598781 -3.651328 29 29 30 NUEMANN 1.948120 -4.449153 4.183324 -2.467780 30 30 31 NUEMANN 4.772719 -2.815470 5.528293 -0.3790777 31 31 32 NUEMANN 5.998548 -0.4113233 5.870877 1.297908 32 32 1 NUEMANN 6.105509 1.349779 5.946890 1.932263 == TOPOGRAPHY FUNCTION(PHAI) AT NODAL POINT== NODAL # X-COORDINATE Y-COORDINATE PHAI-REAL PHAI-IMAG FREE TERM ----------------------------------------------------------------------------------- 1 0.8000000 0.0000000E+00 -0.7361755 1.359247 0.5312500 2 0.7846282 -0.1560723 -0.3727934 1.293470 0.5312500 3 0.7391036 -0.3061468 0.3980593 1.009460 0.5312500 4 0.6651757 -0.4444562 0.8994240 0.4491316 0.5312499 5 0.5656855 -0.5656855 0.7246010 -0.1332707 0.5312501 6 0.4444562 -0.6651757 0.1540354 -0.3331694 0.5312500 7 0.3061467 -0.7391036 -0.1435011 -0.1201803 0.5312499 8 0.1560722 -0.7846283 0.8973557E-01 0.3935234E-01 0.5312501 9 -0.3496911E-07 -0.8000000 0.3848693 -0.2030028 0.5312500 10 -0.1560723 -0.7846282 0.2046812 -0.5710618 0.5312499 11 -0.3061468 -0.7391036 -0.3463505 -0.5546291 0.5312501 12 -0.4444563 -0.6651756 -0.7372459 -0.7791219E-01 0.5312499 13 -0.5656855 -0.5656855 -0.6810671 0.5033375 0.5312500 14 -0.6651757 -0.4444562 -0.3225252 0.8737064 0.5312500 15 -0.7391037 -0.3061466 0.5973844E-01 0.9940131 0.5312500 16 -0.7846283 -0.1560722 0.3062750 0.9874534 0.5312500 17 -0.8000000 0.6993822E-07 0.3866537 0.9712370 0.5312500 18 -0.7846282 0.1560724 0.3062746 0.9874535 0.5312500 19 -0.7391036 0.3061467 0.5973787E-01 0.9940132 0.5312500 20 -0.6651756 0.4444562 -0.3225259 0.8737062 0.5312500 21 -0.5656853 0.5656855 -0.6810675 0.5033373 0.5312500 22 -0.4444560 0.6651759 -0.7372454 -0.7791376E-01 0.5312501 23 -0.3061465 0.7391037 -0.3463493 -0.5546299 0.5312499 24 -0.1560723 0.7846282 0.2046810 -0.5710618 0.5312500 25 0.9539905E-08 0.8000000 0.3848692 -0.2030026 0.5312500 26 0.1560723 0.7846282 0.8973512E-01 0.3935244E-01 0.5312500 27 0.3061469 0.7391036 -0.1435010 -0.1201804 0.5312500 28 0.4444563 0.6651756 0.1540362 -0.3331694 0.5312501 29 0.5656856 0.5656852 0.7246019 -0.1332700 0.5312499 30 0.6651757 0.4444562 0.8994239 0.4491314 0.5312500 31 0.7391037 0.3061467 0.3980587 1.009460 0.5312500 32 0.7846283 0.1560722 -0.3727943 1.293470 0.5312500 == ELEMENT INFORMATION AND SOLUTION OF HEAT FLUX == ELEMENT # FLUX(1)-REAL FLUX(1)-IMAG FLUX(2)-REAL HLUX(2)-IMAG --------------------------------------------------------------------------- 1 5.946890 1.932263 6.105510 1.349776 2 5.870878 1.297905 5.998548 -0.4113262 3 5.528293 -0.3790803 4.772719 -2.815470 4 4.183325 -2.467781 1.948115 -4.449157 5 1.598776 -3.651328 -1.363020 -3.745725 6 -1.012815 -2.783323 -2.779467 -1.023351 7 -1.711589 -0.6301774 -1.515396 1.015006 8 -0.5116851 0.3427246 0.1353149E-06 0.6158586 9 -0.1353154E-06 -0.6158609 -0.5116872 -0.3427257 10 -1.515394 -1.015004 -1.711587 0.6301776 11 -2.779469 1.023354 -1.012813 2.783327 12 -1.363017 3.745726 1.598776 3.651328 13 1.948114 4.449156 4.183324 2.467781 14 4.772719 2.815470 5.528293 0.3790777 15 5.998549 0.4113234 5.870878 -1.297908 16 6.105509 -1.349779 5.946890 -1.932263 17 5.946890 -1.932263 6.105510 -1.349776 18 5.870878 -1.297905 5.998548 0.4113261 19 5.528293 0.3790803 4.772718 2.815473 20 4.183323 2.467783 1.948111 4.449158 21 1.598774 3.651330 -1.363024 3.745724 22 -1.012817 2.783321 -2.779467 1.023347 23 -1.711588 0.6301740 -1.515395 -1.015003 24 -0.5116871 -0.3427253 0.3691530E-07 -0.6158606 25 -0.3691530E-07 0.6158606 -0.5116872 0.3427252 26 -1.515397 1.015005 -1.711589 -0.6301790 27 -2.779467 -1.023354 -1.012812 -2.783326 28 -1.363017 -3.745729 1.598781 -3.651328 29 1.948120 -4.449153 4.183324 -2.467780 30 4.772719 -2.815470 5.528293 -0.3790777 31 5.998548 -0.4113233 5.870877 1.297908 32 6.105509 1.349779 5.946890 1.932263 === TOPOGRAPHY FUNCTION AT INTERNAL POINTS === POINT # X-COORDINATE Y-COORDINATE PHAI-REAL PHAI-IMAG FREE TERM -------------------------------------------------------------------------- 1 1.0000 0.00000E+00 -1.570291 0.1537238 1.00000 2 2.0000 0.00000E+00 -0.9801144 0.6453974 1.00000 3 3.0000 0.00000E+00 -0.6911972 0.6131049 1.00000 4 4.0000 0.00000E+00 -0.5466468 0.5543345 1.00000 5 5.0000 0.00000E+00 -0.4647692 0.5210240 1.00000 ==== WAVE HEIGHT COEFFICIENT K-PRIME ==== LENGTH ALONG BOUNADRY K-PRIME ---------------------------------------- 0.0000000000 0.5908334068 0.1568274281 0.3537594092 0.3136548748 0.3298597369 0.4704822819 0.5683545754 0.6273096988 0.5676229005 0.7841371765 0.7857314567 0.9409645554 0.9532257756 1.0977920622 1.0839133808 1.2546194452 1.3996690108 1.4114468385 1.5952263885 1.5682743423 1.6455550311 1.7251018300 1.7287257588 1.8819291169 1.8354124272 2.0387565946 1.9235857762 2.1955841349 1.9916892713 2.3524114359 2.0321026304 2.5092389130 2.0443018471 2.6660664051 2.0321026621 2.8228936949 1.9916892833 2.9797212089 1.9235858552 3.1365486635 1.8354125803 3.2933762021 1.7287254600 3.4502036599 1.6455551057 3.6070307725 1.5952263587 3.7638582547 1.3996687815 3.9206857476 1.0839131539 4.0775132543 0.9532257564 4.2343406876 0.7857310259 4.3911682409 0.5676227016 4.5479953140 0.5683546023 4.7048228280 0.3298594962 4.8616503175 0.3537597094