Benchmark # 1 -- runup on a uniformly sloping beach: 1-D problem. Compute the snap shots of water-surface and velocity profiles at t = 160 sec., 175 sec, and 220 sec. Also compute the temporal variations of the shoreline location (xs) and shoreline velocity (us) from t = 100 sec. to 280 sec. Beach slope = 1/10 Initial water surface displacement, and velocity = 0, everywhere at t = 0. x (m) eta (m) 0 0.001386879 50 0.001418557 100 0.001448675 150 0.001476851 200 0.001502653 250 0.001525595 300 0.001545127 350 0.001560637 400 0.001571436 450 0.001576752 500 0.001575726 550 0.0015674 600 0.001550705 650 0.001524456 700 0.001487337 750 0.001437888 800 0.001374497 850 0.001295378 900 0.001198562 950 0.00108188 1000 0.000942942 1050 0.000779122 1100 0.000587533 1150 0.000365013 1200 0.000108095 1250 -0.000187012 1300 -0.000524455 1350 -0.000908755 1400 -0.001344846 1450 -0.001838098 1500 -0.002394354 1550 -0.00301996 1600 -0.003721805 1650 -0.004507353 1700 -0.005384687 1750 -0.006362547 1800 -0.007450373 1850 -0.008658349 1900 -0.009997448 1950 -0.011479481 2000 -0.013117144 2050 -0.014924068 2100 -0.016914873 2150 -0.019105216 2200 -0.021511848 2250 -0.024152665 2300 -0.027046767 2350 -0.030214509 2400 -0.033677557 2450 -0.037458945 2500 -0.041583128 2550 -0.046076034 2600 -0.050965122 2650 -0.056279425 2700 -0.062049605 2750 -0.068307999 2800 -0.075088659 2850 -0.082427396 2900 -0.090361815 2950 -0.098931345 3000 -0.10817727 3050 -0.118142745 3100 -0.128872819 3150 -0.140414434 3200 -0.152816431 3250 -0.166129544 3300 -0.180406381 3350 -0.195701401 3400 -0.212070878 3450 -0.229572857 3500 -0.248267096 3550 -0.268215 3600 -0.289479539 3650 -0.312125157 3700 -0.336217664 3750 -0.361824121 3800 -0.389012704 3850 -0.417852558 3900 -0.44841364 3950 -0.480766537 4000 -0.514982285 4050 -0.55113216 4100 -0.589287466 4150 -0.629519299 4200 -0.671898307 4250 -0.716494437 4300 -0.763376645 4350 -0.812612645 4400 -0.8642686 4450 -0.918408824 4500 -0.975095469 4550 -1.034388211 4600 -1.096343923 4650 -1.161016343 4700 -1.228455744 4750 -1.298708591 4800 -1.371817204 4850 -1.447819424 4900 -1.526748269 4950 -1.608631608 5000 -1.693491827 5050 -1.781345512 5100 -1.872203133 5150 -1.966068741 5200 -2.062939676 5250 -2.162806291 5300 -2.265651683 5350 -2.371451433 5400 -2.480173427 5450 -2.59177757 5500 -2.70621564 5550 -2.823431106 5600 -2.94335898 5650 -3.06592569 5700 -3.191048978 5750 -3.318637827 5800 -3.448592406 5850 -3.58080405 5900 -3.715155257 5950 -3.851519724 6000 -3.989762401 6050 -4.129739578 6100 -4.271298998 6150 -4.414279999 6200 -4.558513686 6250 -4.703823128 6300 -4.850023589 6350 -4.996922778 6400 -5.144321137 6450 -5.292012151 6500 -5.439782687 6550 -5.58741336 6600 -5.734678926 6650 -5.881348704 6700 -6.02718702 6750 -6.171953678 6800 -6.315404461 6850 -6.457291647 6900 -6.597364561 6950 -6.735370141 7000 -6.871053531 7050 -7.004158697 7100 -7.13442906 7150 -7.261608157 7200 -7.385440311 7250 -7.505671328 7300 -7.622049208 7350 -7.73432487 7400 -7.842252895 7450 -7.945592275 7500 -8.044107177 7550 -8.137567719 7600 -8.225750741 7650 -8.308440589 7700 -8.385429907 7750 -8.456520381 7800 -8.521523565 7850 -8.580261612 7900 -8.632568033 7950 -8.678288437 8000 -8.717281245 8050 -8.749418381 8100 -8.774585933 8150 -8.792684782 8200 -8.803631188 8250 -8.807357334 8300 -8.803811821 8350 -8.792960111 8400 -8.774784909 8450 -8.74928648 8500 -8.716482902 8550 -8.676410242 8600 -8.629122662 8650 -8.574692438 8700 -8.513209897 8750 -8.444783276 8800 -8.369538491 8850 -8.287618787 8900 -8.199184364 8950 -8.104411852 9000 -8.003493726 9050 -7.896637634 9100 -7.784065634 9150 -7.666013357 9200 -7.542729099 9250 -7.414472831 9300 -7.28151516 9350 -7.144136223 9400 -7.002624539 9450 -6.857275816 9500 -6.708391729 9550 -6.55627867 9600 -6.401246492 9650 -6.243607241 9700 -6.083673894 9750 -5.921759116 9800 -5.758174032 9850 -5.593227037 9900 -5.427222643 9950 -5.26046037 10000 -5.093233695 10050 -4.925829065 10100 -4.758524964 10150 -4.591591061 10200 -4.42528743 10250 -4.259863844 10300 -4.095559149 10350 -3.932600726 10400 -3.77120402 10450 -3.611572165 10500 -3.453895679 10550 -3.298352239 10600 -3.145106536 10650 -2.994310197 10700 -2.846101782 10750 -2.700606845 10800 -2.557938053 10850 -2.418195373 10900 -2.281466301 10950 -2.147826147 11000 -2.01733836 11050 -1.890054895 11100 -1.76601661 11150 -1.645253691 11200 -1.527786148 11250 -1.413624219 11300 -1.302768919 11350 -1.195212528 11400 -1.090939108 11450 -0.989925023 11500 -0.892139465 11550 -0.797544971 11600 -0.706097946 11650 -0.617749174 11700 -0.532444323 11750 -0.450124438 11800 -0.37072642 11850 -0.2941835 11900 -0.220425684 11950 -0.149380187 12000 -0.080971874 12050 -0.015123622 12100 0.048243274 12150 0.109208742 12200 0.167853593 12250 0.224259202 12300 0.278507202 12350 0.330679203 12400 0.38085653 12450 0.429119979 12500 0.475549594 12550 0.520224462 12600 0.563222526 12650 0.604620415 12700 0.644493293 12750 0.682914725 12800 0.719956554 12850 0.755688801 12900 0.790179575 12950 0.823494994 13000 0.855699125 13050 0.886853934 13100 0.917019246 13150 0.946252721 13200 0.974609831 13250 1.002143855 13300 1.028905882 13350 1.054944815 13400 1.08030739 13450 1.105038199 13500 1.129179719 13550 1.152772344 13600 1.175854426 13650 1.19846232 13700 1.220630429 13750 1.242391253 13800 1.263775447 13850 1.284811872 13900 1.305527654 13950 1.325948243 14000 1.346097472 14050 1.365997618 14100 1.385669461 14150 1.40513235 14200 1.424404255 14250 1.443501836 14300 1.462440499 14350 1.481234451 14400 1.499896764 14450 1.518439428 14500 1.536873406 14550 1.555208689 14600 1.573454347 14650 1.591618579 14700 1.609708764 14750 1.627731507 14800 1.645692682 14850 1.663597478 14900 1.681450441 14950 1.699255512 15000 1.717016065 15050 1.734734946 15100 1.752414505 15150 1.770056627 15200 1.787662769 15250 1.805233984 15300 1.82277095 15350 1.840273998 15400 1.857743134 15450 1.875178066 15500 1.892578223 15550 1.909942775 15600 1.927270656 15650 1.944560578 15700 1.961811051 15750 1.979020396 15800 1.996186764 15850 2.013308145 15900 2.030382385 15950 2.047407193 16000 2.064380161 16050 2.081298763 16100 2.098160374 16150 2.114962276 16200 2.131701664 16250 2.148375657 16300 2.164981307 16350 2.181515598 16400 2.197975461 16450 2.214357776 16500 2.230659377 16550 2.246877059 16600 2.26300758 16650 2.27904767 16700 2.294994031 16750 2.310843342 16800 2.326592264 16850 2.342237442 16900 2.35777551 16950 2.373203091 17000 2.388516803 17050 2.403713262 17100 2.41878908 17150 2.433740874 17200 2.448565264 17250 2.463258875 17300 2.477818341 17350 2.492240309 17400 2.506521436 17450 2.520658395 17500 2.534647874 17550 2.54848658 17600 2.562171241 17650 2.575698605 17700 2.589065444 17750 2.602268555 17800 2.615304762 17850 2.628170916 17900 2.640863898 17950 2.65338062 18000 2.665718025 18050 2.677873093 18100 2.689842836 18150 2.701624304 18200 2.713214585 18250 2.724610805 18300 2.735810131 18350 2.746809772 18400 2.757606981 18450 2.768199051 18500 2.778583325 18550 2.788757189 18600 2.798718078 18650 2.808463476 18700 2.817990916 18750 2.827297982 18800 2.83638231 18850 2.845241588 18900 2.853873559 18950 2.862276021 19000 2.870446825 19050 2.878383883 19100 2.886085162 19150 2.893548687 19200 2.900772544 19250 2.907754877 19300 2.914493892 19350 2.920987859 19400 2.927235105 19450 2.933234026 19500 2.938983077 19550 2.944480781 19600 2.949725724 19650 2.954716558 19700 2.959452001 19750 2.963930838 19800 2.968151923 19850 2.972114175 19900 2.975816582 19950 2.979258201 20000 2.982438159 20050 2.985355651 20100 2.98800994 20150 2.990400364 20200 2.992526325 20250 2.9943873 20300 2.995982835 20350 2.997312547 20400 2.998376124 20450 2.999173324 20500 2.999703978 20550 2.999967986 20600 2.999965321 20650 2.999696026 20700 2.999160217 20750 2.998358077 20800 2.997289863 20850 2.995955903 20900 2.994356594 20950 2.992492403 21000 2.990363869 21050 2.987971598 21100 2.985316269 21150 2.982398627 21200 2.979219488 21250 2.975779735 21300 2.972080318 21350 2.968122258 21400 2.96390664 21450 2.959434617 21500 2.954707406 21550 2.949726292 21600 2.944492623 21650 2.939007812 21700 2.933273336 21750 2.927290733 21800 2.921061605 21850 2.914587616 21900 2.907870488 21950 2.900912004 22000 2.893714009 22050 2.886278402 22100 2.878607142 22150 2.870702244 22200 2.862565779 22250 2.854199872 22300 2.845606703 22350 2.836788504 22400 2.827747559 22450 2.818486204 22500 2.809006824 22550 2.799311854 22600 2.789403774 22650 2.779285116 22700 2.768958452 22750 2.758426404 22800 2.747691633 22850 2.736756847 22900 2.72562479 22950 2.714298252 23000 2.702780057 23050 2.691073071 23100 2.679180194 23150 2.667104362 23200 2.654848547 23250 2.642415751 23300 2.629809013 23350 2.617031396 23400 2.604085999 23450 2.590975945 23500 2.577704385 23550 2.564274497 23600 2.550689483 23650 2.536952567 23700 2.523066996 23750 2.509036039 23800 2.494862982 23850 2.480551132 23900 2.466103811 23950 2.451524357 24000 2.436816124 24050 2.421982477 24100 2.407026795 24150 2.391952467 24200 2.376762891 24250 2.361461475 24300 2.346051632 24350 2.330536781 24400 2.314920348 24450 2.299205759 24500 2.283396444 24550 2.267495835 24600 2.251507362 24650 2.235434454 24700 2.219280538 24750 2.203049036 24800 2.186743366 24850 2.17036694 24900 2.153923164 24950 2.137415433 25000 2.120847134 25050 2.104221643 25100 2.087542326 25150 2.070812535 25200 2.054035608 25250 2.037214869 25300 2.020353625 25350 2.003455168 25400 1.986522771 25450 1.969559689 25500 1.952569155 25550 1.935554385 25600 1.918518571 25650 1.901464882 25700 1.884396465 25750 1.867316442 25800 1.85022791 25850 1.83313394 25900 1.816037576 25950 1.798941834 26000 1.781849703 26050 1.764764141 26100 1.747688077 26150 1.73062441 26200 1.713576006 26250 1.696545701 26300 1.679536296 26350 1.662550559 26400 1.645591227 26450 1.628660998 26500 1.611762539 26550 1.594898478 26600 1.578071408 26650 1.561283886 26700 1.544538431 26750 1.527837523 26800 1.511183606 26850 1.494579083 26900 1.478026321 26950 1.461527644 27000 1.44508534 27050 1.428701653 27100 1.412378788 27150 1.396118911 27200 1.379924144 27250 1.363796569 27300 1.347738226 27350 1.331751115 27400 1.31583719 27450 1.299998367 27500 1.284236516 27550 1.268553468 27600 1.252951008 27650 1.23743088 27700 1.221994785 27750 1.206644381 27800 1.191381282 27850 1.176207061 27900 1.161123246 27950 1.146131323 28000 1.131232734 28050 1.116428881 28100 1.101721119 28150 1.087110763 28200 1.072599084 28250 1.058187312 28300 1.043876633 28350 1.029668191 28400 1.015563088 28450 1.001562384 28500 0.987667098 28550 0.973878206 28600 0.960196644 28650 0.946623306 28700 0.933159047 28750 0.919804678 28800 0.906560973 28850 0.893428665 28900 0.880408447 28950 0.867500972 29000 0.854706856 29050 0.842026675 29100 0.829460966 29150 0.817010231 29200 0.80467493 29250 0.79245549 29300 0.7803523 29350 0.76836571 29400 0.756496039 29450 0.744743567 29500 0.733108539 29550 0.721591168 29600 0.710191629 29650 0.698910068 29700 0.687746594 29750 0.676701284 29800 0.665774186 29850 0.654965311 29900 0.644274643 29950 0.633702133 30000 0.623247703 30050 0.612911246 30100 0.602692623 30150 0.592591668 30200 0.582608189 30250 0.572741963 30300 0.562992741 30350 0.553360248 30400 0.543844184 30450 0.534444221 30500 0.525160009 30550 0.51599117 30600 0.506937307 30650 0.497997995 30700 0.48917279 30750 0.480461223 30800 0.471862806 30850 0.463377028 30900 0.455003358 30950 0.446741246 31000 0.438590122 31050 0.430549396 31100 0.422618462 31150 0.414796694 31200 0.40708345 31250 0.399478071 31300 0.391979882 31350 0.384588193 31400 0.377302298 31450 0.370121476 31500 0.363044993 31550 0.356072102 31600 0.349202042 31650 0.342434038 31700 0.335767307 31750 0.329201052 31800 0.322734465 31850 0.316366727 31900 0.310097012 31950 0.30392448 32000 0.297848286 32050 0.291867575 32100 0.285981483 32150 0.28018914 32200 0.274489668 32250 0.268882181 32300 0.263365791 32350 0.257939599 32400 0.252602704 32450 0.247354198 32500 0.242193171 32550 0.237118706 32600 0.232129885 32650 0.227225784 32700 0.222405478 32750 0.217668039 32800 0.213012537 32850 0.208438039 32900 0.203943613 32950 0.199528323 33000 0.195191234 33050 0.190931411 33100 0.186747918 33150 0.18263982 33200 0.178606182 33250 0.17464607 33300 0.170758552 33350 0.166942696 33400 0.163197575 33450 0.159522259 33500 0.155915825 33550 0.152377351 33600 0.148905918 33650 0.14550061 33700 0.142160514 33750 0.138884723 33800 0.13567233 33850 0.132522435 33900 0.129434142 33950 0.126406559 34000 0.1234388 34050 0.120529981 34100 0.117679227 34150 0.114885667 34200 0.112148433 34250 0.109466666 34300 0.106839512 34350 0.104266122 34400 0.101745655 34450 0.099277274 34500 0.096860151 34550 0.094493463 34600 0.092176394 34650 0.089908134 34700 0.087687883 34750 0.085514845 34800 0.083388232 34850 0.081307265 34900 0.079271169 34950 0.07727918 35000 0.07533054 35050 0.073424497 35100 0.071560311 35150 0.069737245 35200 0.067954573 35250 0.066211576 35300 0.064507542 35350 0.062841768 35400 0.06121356 35450 0.05962223 35500 0.058067099 35550 0.056547497 35600 0.05506276 35650 0.053612234 35700 0.052195273 35750 0.05081124 35800 0.049459503 35850 0.048139441 35900 0.046850441 35950 0.045591897 36000 0.044363213 36050 0.043163799 36100 0.041993075 36150 0.040850469 36200 0.039735416 36250 0.038647359 36300 0.037585751 36350 0.036550051 36400 0.035539728 36450 0.034554257 36500 0.033593122 36550 0.032655815 36600 0.031741836 36650 0.030850693 36700 0.029981899 36750 0.02913498 36800 0.028309465 36850 0.027504892 36900 0.026720809 36950 0.025956767 37000 0.025212329 37050 0.024487062 37100 0.023780543 37150 0.023092354 37200 0.022422086 37250 0.021769336 37300 0.021133708 37350 0.020514815 37400 0.019912273 37450 0.01932571 37500 0.018754757 37550 0.018199053 37600 0.017658243 37650 0.017131981 37700 0.016619923 37750 0.016121737 37800 0.015637093 37850 0.015165668 37900 0.014707148 37950 0.014261223 38000 0.013827587 38050 0.013405945 38100 0.012996004 38150 0.012597478 38200 0.012210087 38250 0.011833556 38300 0.011467616 38350 0.011112004 38400 0.010766462 38450 0.010430738 38500 0.010104584 38550 0.009787757 38600 0.009480021 38650 0.009181144 38700 0.0088909 38750 0.008609065 38800 0.008335422 38850 0.00806976 38900 0.00781187 38950 0.007561549 39000 0.007318599 39050 0.007082824 39100 0.006854036 39150 0.006632048 39200 0.00641668 39250 0.006207753 39300 0.006005094 39350 0.005808536 39400 0.005617911 39450 0.005433059 39500 0.005253823 39550 0.005080047 39600 0.004911583 39650 0.004748283 39700 0.004590004 39750 0.004436607 39800 0.004287955 39850 0.004143915 39900 0.004004358 39950 0.003869157 40000 0.003738188 40050 0.003611331 40100 0.003488469 40150 0.003369488 40200 0.003254275 40250 0.003142722 40300 0.003034723 40350 0.002930175 40400 0.002828977 40450 0.002731032 40500 0.002636243 40550 0.002544518 40600 0.002455766 40650 0.002369899 40700 0.002286831 40750 0.002206478 40800 0.00212876 40850 0.002053596 40900 0.00198091 40950 0.001910627 41000 0.001842674 41050 0.00177698 41100 0.001713475 41150 0.001652093 41200 0.001592769 41250 0.001535438 41300 0.001480039 41350 0.001426512 41400 0.001374799 41450 0.001324842 41500 0.001276588 41550 0.001229981 41600 0.001184971 41650 0.001141507 41700 0.001099538 41750 0.001059019 41800 0.001019903 41850 0.000982143 41900 0.000945698 41950 0.000910524 42000 0.000876581 42050 0.000843827 42100 0.000812226 42150 0.000781738 42200 0.000752328 42250 0.00072396 42300 0.0006966 42350 0.000670214 42400 0.00064477 42450 0.000620238 42500 0.000596585 42550 0.000573784 42600 0.000551804 42650 0.00053062 42700 0.000510204 42750 0.000490529 42800 0.000471572 42850 0.000453306 42900 0.00043571 42950 0.000418759 43000 0.000402432 43050 0.000386707 43100 0.000371563 43150 0.000356981 43200 0.000342941 43250 0.000329423 43300 0.000316411 43350 0.000303885 43400 0.000291829 43450 0.000280227 43500 0.000269061 43550 0.000258318 43600 0.000247982 43650 0.000238038 43700 0.000228473 43750 0.000219272 43800 0.000210423 43850 0.000201914 43900 0.000193731 43950 0.000185863 44000 0.0001783 44050 0.000171028 44100 0.000164039 44150 0.000157321 44200 0.000150865 44250 0.000144661 44300 0.0001387 44350 0.000132973 44400 0.00012747 44450 0.000122185 44500 0.000117109 44550 0.000112233 44600 0.000107551 44650 0.000103055 44700 9.87377E-05 44750 9.45932E-05 44800 9.06147E-05 44850 8.67957E-05 44900 8.31303E-05 44950 7.96127E-05 45000 7.62371E-05 45050 7.29981E-05 45100 6.98906E-05 45150 6.69094E-05 45200 6.40496E-05 45250 6.13066E-05 45300 5.86759E-05 45350 5.61531E-05 45400 5.3734E-05 45450 5.14145E-05 45500 4.91908E-05 45550 4.7059E-05 45600 4.50157E-05 45650 4.30572E-05 45700 4.11803E-05 45750 3.93817E-05 45800 3.76583E-05 45850 3.60072E-05 45900 3.44253E-05 45950 3.29101E-05 46000 3.14587E-05 46050 3.00687E-05 46100 2.87375E-05 46150 2.74628E-05 46200 2.62423E-05 46250 2.50739E-05 46300 2.39553E-05 46350 2.28846E-05 46400 2.18598E-05 46450 2.08791E-05 46500 1.99405E-05 46550 1.90425E-05 46600 1.81833E-05 46650 1.73613E-05 46700 1.6575E-05 46750 1.5823E-05 46800 1.51037E-05 46850 1.44158E-05 46900 1.3758E-05 46950 1.3129E-05 47000 1.25278E-05 47050 1.19529E-05 47100 1.14035E-05 47150 1.08783E-05 47200 1.03764E-05 47250 9.89677E-06 47300 9.43847E-06 47350 9.0006E-06 47400 8.58228E-06 47450 8.18267E-06 47500 7.80097E-06 47550 7.43642E-06 47600 7.08828E-06 47650 6.75583E-06 47700 6.4384E-06 47750 6.13535E-06 47800 5.84603E-06 47850 5.56987E-06 47900 5.30628E-06 47950 5.05471E-06 48000 4.81464E-06 48050 4.58557E-06 48100 4.36701E-06 48150 4.15849E-06 48200 3.95958E-06 48250 3.76985E-06 48300 3.58889E-06 48350 3.41631E-06 48400 3.25175E-06 48450 3.09483E-06 48500 2.94523E-06 48550 2.80261E-06 48600 2.66665E-06 48650 2.53707E-06 48700 2.41357E-06 48750 2.29588E-06 48800 2.18373E-06 48850 2.07688E-06 48900 1.97507E-06 48950 1.8781E-06 49000 1.78572E-06 49050 1.69774E-06 49100 1.61395E-06 49150 1.53415E-06 49200 1.45818E-06 49250 1.38584E-06 49300 1.31697E-06 49350 1.25142E-06 49400 1.18902E-06 49450 1.12963E-06 49500 1.07312E-06 49550 1.01934E-06 49600 9.68169E-07 49650 9.19486E-07 49700 8.73173E-07 49750 8.29119E-07 49800 7.87218E-07 49850 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