NUMERICAL SIMULATION OF TSUNAMI CURRENTS AROUND MOVING STRUCTURES

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1 NUMERICAL SIMULATION OF TSUNAMI CURRENTS AROUND MOVING STRUCTURES Ezo Nakaza 1, Tsuakyo Ibe ad Muhammad Abdu Rouf 1 The pape ams to smulate Tsuam cuets aoud movg ad fxed stuctues usg the movg-patcle semmplct method. A ope chael wth fou dffeet sets of stuctues s employed the umecal model. The smulato esults fo the case wth oe stuctue dcate that the flow aoud the movg stuctue s faste tha that aoud the fxed stuctue. The flow becomes moe complex fo cases wth addtoal stuctues. Keywods: umecal smulato; Tsuam cuets; boe; movg stuctues INTRODUCTION Tsuam s a well kow pheomeo that ofte stke coastal aeas ad dowed vaous types of stuctues. The heght ad dstace of swashed debs fom the coast as well as the stegth ad uup heght of tsuams ae usually estmated by eseaches. Estmatg the tsuam-duced cuets aoud stuctues ad as a cosequece, the movg pattes of the stuctues ae vey complex. The estmato of such complex cuets ad behavos of dowed stuctues ae mpotat fo desgg coastal stuctues wth the vew of makg coutemeasues agast tsuam attacks. I ode to clafy such complex cuets aoud movg thee-dmesoal stuctues as well as the teactos betwee the cuets ad the movg stuctues, the movg-patcle sem-mplct method (MPSM) s toduced hee. MPSM The movg patcle sem-mplct method (MPSM) s a modfed patcle method developed by Koshzuka ad Oka (1996) fo solvg a compessble flow. Ths method s sutable fo smulato of complex fee suface moto because the method does ot use gds. Futhemoe, sce ths method s a Lagaga method, the calculato of advecto tems s ot equed. The MPSM has bee successfully appled to wave beakg (Koshzuka et al. 1998), shppg wate o the deck of a shp (Shbata et al. 9), ad valdatg pessue (Khayye ad Gotoh 8) as coastal egeeg poblems. The MPSM ca be descbed as follows. Dscetzato Method Weght fucto. The MPSM uses a model of teacto amog patcles fo dscetzg a dffeetal opeato. The teacto betwee patcle ad ts eghbog patcle volves a weght fucto w, as follows: I Eq. (1), s the dstace betwee patcles e 1 e (1) w() e < epeseted by paamete e. The patcle umbe desty s defed as ad, ad the adus of the teacto aea s ( ) w () whch s the sum of the weght fucto of eghbog patcle. I Eq. (), the cotbuto fom patcle s ot cosdeed. The tal patcle umbe desty s calculated fo the tal patcle postos, whch ae usually gve as a squae lattce. Gadet model the MPS method. A gadet vecto at patcle that has scala quatty φ s calculated usg the followg equato: 1 Faculty of Egeeg, Uvesty of the Ryukyus, 1 Sebau, Nshhaa, Okawa, 93-13, Japa DPRCIR, Uvesty of the Ryukyus, 1 Sebau, Nshhaa, Okawa, 93-13, Japa 1

2 COASTAL ENGINEERING 1 φ d φ φ ( ) w( ) (3) φ s a abtay physcal quatty, d s the umbe of dmesos, whee umbe desty, ad w s the weght fucto. s the tal patcle Laplaca model the MPSM. Physcal quattes of patcle ae dstbuted to eghbog patcle usg the weght fucto the followg equato: [ ( φ φ ) w( )] d φ (4) λ whee λ s a coeffcet toduced to cotol the cease vaace to agee wth that of the aalytc soluto, gve as follows: λ w w ( ) ( ) Fo ths poblem, statstcs dcate that the vaace ceases lealy wth tme. Calculato algothm A sem-mplct algothm s appled to the compessble Nave-Stokes equato: u 1 p + ν u + F (6) t ρ whee ρ s the flud desty ad ν s the kematc vscosty. I a tme step, the exteal foce, vscosty, ad pessue gadet tems ae calculated explctly. The Posso equato of pessue s calculated mplctly usg a teato solve. Fst, the exteal foce ad vscosty tems of the Nave-Stokes equato ae calculated explctly, ad the tempoay velocty u s obtaed as follows: k k u u + ν u dt + Fdt (7) whee dt s the tme cemet. The tempoay patcle posto k + u dt (8) (5) s calculated as follows: The tempoay patcle umbe desty s evaluated fom the tempoay posto ad devates fom the tal patcle umbe desty. I ths case, the flud desty s ot costat. Theefoe, the pessues of the patcles ae calculated such that they etu to the tal patcle umbe desty. ' dt u (9) The coecto velocty ' u s calculated usg the pessue gadet tem: u ' k 1 P +1 dt (1) ρ Substtutg Eq. (1) to Eq. (9), we obta the Posso equato fo pessue: k 1 P + ρ (11) dt k +1 k +1 The ew tme pessue p s obtaed by solvg Eq. (11). Substtutg p to Eq. (1), we obta the coecto velocty. Ths coecto velocty s the added to the tempoay velocty: u + u + u (1) k 1 '

3 COASTAL ENGINEERING 1 3 I the ed, the coecto dsplacemet s added to the tempoay posto: k + 1 ' + u dt (13) NUMERICAL SIMULATION As a umecal smulato, the MPSM has bee appled to smulate the cuet wth stuctues o a chael. These smulatos deal wth both fxed ad movg gd bodes. The cuet s assumed to be tsuam boe ad tsuam u-up, ad the gd bodes ae assumed to be a boke coastal stuctue, a ca, ad ubble. Numecal model Plae ad coss-sectoal vews of the chael model used hee as a umecal model ae show Fg Up-steam 5 Dow-steam Left ed of the chael Posto of the cocete blocks (a) Plae vew (legth: m) (b-1) Cases 1 ad (b-) Case (b-3) Case (b-4) Dmesos of the block (b) Coss-sectoal vew ad dmesos of the block (legth: m) Fgue 1. Plae ad coss-sectoal vews of the model Fg. 1(a) shows a plae vew of the chael. The wdth of the chael s 5. m, ad the total legth s 41 m. Cocete blocks ae placed o the posto of 1 m dowwad fom the left ed of the chael. Fg. 1(b) shows a coss-sectoal vew ad the aagemets of the cocete blocks. Fou cases wth dffeet aagemets of cocete blocks wee examed (desty:,3 kg/m 3, statc fcto:.4, dyamc fcto:.3). I the fst case (Case 1), a sgle cocete block s fxed. I Case, a sgle moveable cocete block s placed the chael. I Case 3, thee blocks that ca be moved by the cuet ae placed the chael. Fally, Case 4, sx blocks stacked two blocks hgh ae placed the chael. The aagemets of Cases 1 though 4 ae show Fgs. 1(b-1) though 1(b-3). The dmesos of the blocks ae show Fg. 1(b-4). Table 1 shows the computatoal vaables ad the bouday codto. The tal boe heght s 1 m, ad the velocty s.5 m/s. The mateal of the boe s wate. The bouday codto of the wall s the o-slp codto.

4 4 COASTAL ENGINEERING 1 Table 1. Computatoal vaables ad bouday codto. Case Ital wate level.1m Ital boe heght 1m Ital velocty of boe.5m/s Coeffcet of vscosty.1pa s Wall bouday codto No-slp Desty of flud 1,kg/m 3 Desty of block,3kg/m 3 Fcto codto betwee Wall ad block Fx Coeffcet of statc fcto.4 Coeffcet of dyamc fcto.3 Damete of patcle.1m Tme cemet.5s Smulato esults The behavo of the stuctues ad the tsuam cuets ae show Fgs. though 6. I Case 1, the boe umps up due to collso wth the block, as show the bottom pael of Fg. (a). Backwate appeas fot of the stuctue afte 5.5 secods of smulato tme, ad the velocty s foud to be low alog the cete le behd the stuctue ad hgh alog the sdewalls, as show the mddle pael of Fg. (b). I Case, the velocty s vey hgh aoud the sdes of the stuctue, but vey low behd the stuctue (Fg. 3). The velocty was low aoud the fxed block of Case 1, but hgh aoud the movg block of Case. These esults dcate that teacto betwee the flud ad stuctue ceates seveal types of flow aoud stuctues. Ths s a vey mpotat cosdeato whe desgg stuctues to wthstad tsuam boe. Iceased teacto of the blocks wth cuets esults moe complex cuet pattes Cases 3 ad 4. I Case 3, the wate level s hghe tha Case because the stuctue obstucts the pogess of the boe, as show the bottom pael of Fg. 4(a). I ths case, the flow decto s chaged by the otato of the stuctue, as show the mddle laye of Fg. 4(b). I Case 4, the stacks of blocks move faste (Fg. 5) tha the sgle blocks of Case 3 because the stuctues Case 4 obstuct the pogess of the boe ad sgfcatly cease the velocty aoud the stuctue. A close-up vew of the esults fo Case 4 (Fg. 6) dcates that the uppe pat of the stoed blocks have falle dow fot of the base oe secod afte the tsuam. These esults dcate that MPSM s a useful tool fo udestadg complex thee-dmesoal pheomea. Velocty (m/s) (m) (m) [3.3m/s] [.4m/s] [4.m/s] (a) Tme 1.s (b) Tme 5.5s Fgue. Result fo Case 1

5 COASTAL ENGINEERING 1 5 Velocty (m/s) (m) (m) [3.m/s] [.m/s] [4.m/s] (a) Tme 1.s (b) Tme 5.5s Fgue 3. Result fo Case Velocty (m/s) (m) (m) [3.m/s] [4.4m/s] [.5m/s] (a) Tme 1.s (b) Tme 5.5s Fgue 4. Result fo Case 3 Velocty (m/s) (m) (m) [3.4m/s] [.1m/s] [4.5m/s] (a) Tme 1.s (b) Tme 5.5s Fgue 5. Result fo case 4

6 6 COASTAL ENGINEERING 1 Velocty (m/s) (a) Tme.5s (b) Tme 1.s Fgue 6. Close-up of the esults fo Case 4 CONCLUSION The peset study clafes the complex cuet pattes aoud movg thee-dmesoal stuctues usg the MPSM. The smulato study evealed the followg. 1. The flow aoud the movg stuctue s faste tha flow aoud the fxed stuctue.. Addtoal stuctues ad the postos would make the flow moe complex. 3. The MPSM s a vey useful tool to estmate such a complex cuet patte. REFERENCES Koshzuka, S., ad Y. Oka Movg patcle sem-mplct method fo fagmetato of compessble flud, Nuclea Scece ad Egeeg, 13, Koshzuka, S., A. Nobe, ad Y. Oka Numecal aalyss of beakg waves usg the movg patcle sem-mplct method, Iteatoal Joual fo Numecal Method Flud, 6, Shbata, K., S. Koshzuka, ad K. Tazawa. 9. Thee-dmesoal umecal aalyss of shppg wate oto a movg shp usg a patcle method, Joual of Mae Scece ad Techology, 14, Khayye, A., ad H. Gotoh. 9. Modfed movg patcle sem-mplct methods fo the pedcto of D wave mpact pessue, Coastal Egeeg Joual, 56,