URBA N FLO O DS MO DELLING A ND TWO - DIMENSIO NA L SHA LLO W WA TER MO DEL WITH PO RO SITY
Rud i He rma n*
A b stra k
Po la g e na ng a n m e m iliki d a m p a k ya ng sa ng a t b e sa r p a d a wila ya h p e rko ta a n d i d a e ra h d a ta ra n sung a i. Da la m m e m p e rhitung ka n p e rub a ha n d a n p e ng ura ng a n d e b it a kib a t a d a nya b a ng una n d a n ko nstruksi ya ng la in p a d a wila ya h d a ta ra n sung a i, p e ng g una a n m o d e l a lira n d a ng ka l d e ng a n c e la h m e rup a ka n sua tu ha l ya ng d iuta ra ka n. Untuk ha l ini m o d e l sum b e r a ir ya ng khusus untuk m e ng e ksp re sika n ke hila ng a n e ne rg i d a la m wila ya h p e rko ta a n d ip e rluka n. Fo rm ula ya ng d iusulka n a d a la h m e m b a nd ing ka n d a ta uji c o b a ya ng d ip e ro le h d a ri sa lura n la b o ra to rium p a d a ska la ya ng d ise sua ika n d e ng a n wila ya h p e rko ta a n. Pa d a ting ka t a kura si ya ng sa m a , m e to d e ini m e m p e rliha tka n p e nuruna n ya ng sig nifika n d a la m p e rhitung a nnya d ib a nd ing ka n d e ng a n m e ng g una ka n g rid ya ng le b ih ke c il p a d a sim ula si kla sik.
Kata kunc i: d a ta ra n sung a i, mo d e l fisik, mo d e l d ua -d ime nsi
Abstrac t
Flo o d p la ins with urb a n a re a s ha ve sig nific a nt e ffe c ts o n inund a tio n p a tte rns. A sha llo w wa te r mo d e l is p re se nte d, with p o ro sity to a c c o unt fo r the re d uc tio n in sto ra g e a nd in the e xc ha ng e se c tio ns d ue to the p re se nc e o f b uild ing s a nd o the r struc ture s in the flo o d p la ins. A sp e c ific so urc e te rm re p re se nting he a d lo sse s sing ula ritie s in the urb a n a re a s is ne e d e d . The p ro p o se d fo rmula tio n is c o mp a re d to e xp e rime nta l d a ta o b ta ine d fro m c ha nne l e xp e rime nts o n a sc a le o f a n urb a nize d a re a . The me tho d is se e n to re sult in sig nific a nt re d uc tio n o f c o mp uta tio na l e ffo rt c o mp a re d to c la ssic a l simula tio ns using re fine d g rid s, with a simila r d e g re e o f a c c ura c y.
Ke y wo rds: inund a tio n, p hysic a l mo d e l, two -d ime nsio na l mo d e l
* Sta f Pe ng a ja r Jurusa n Te knik Sip il Fa kulta s Te knik Unive rsita s Ta d ula ko , Pa lu
1. Intro d uc tio n
Urb a n a re a s a re o fte n vulne ra b le b e c a use o f the c o njunc tio n o f a hig h c o nc e ntra tio n o f inha b ita nt a nd e c o no m ic a c to rs a nd a ha za rd o us c o nte xt (im p e rvio us a re a s, p ro xim ity o f rive rs e tc ). A p re ve ntio n a p p ro a c h le a d s to the d e ve lo p m e nt o f flo o d m a p p ing , with va rio us a p p lic a tio ns in the fie ld o f urb a n e ng ine e ring : kno wle d g e o f e xp o sure to risk, re g ula tio n o f urb a n p la nning , e la b o ra tio n o f c risis m a na g e m e nt sc e na rio s fo r e xa m p le . Am o ng the e xisting num e ric a l m o d e ls, two -d im e nsio na l sha llo w wa te r m o d e ls se e m to b e the b e st c o m p ro m ise b e twe e n flo w d e sc rip tio n, d a ta ne e d s
a nd c o m p uta tio na l tim e . Ho we ve r, c o nsid e ring la rg e urb a n a re a s c a n le a d to a d ra m a tic inc re a se o f b o th c o m p uta tio na l c e ll num b e r a nd tim e .
c o e ffic ie nt, o r to use the lo c a l he a d -lo sse s fo rm ula tio n o f Eg . (4). The first so lutio n is no t p hysic a lly a p p ro p ria te b e c a use Stric kle r fo rm ula tio n is va lid fo r turb ule nt she a r stre ss within the b o und a ry la ye r a t the b o tto m a nd wa lls,
whe re a s lo c a l he a d -lo sse s a re a ssum e d to b e id e ntic a l o ve r the e ntire flo w c ro ss-se c tio n a nd sho uld the re fo re sim p ly b e p ro p o rtio na l to the sq ua re o f the ve lo c itie s invo lve d [3].
Ta b le 1. C ha ra c te ristic m e sh, c e lls num b e r a nd c o m p uta tio na l tim e fo r e a c h sim ula tio n.
De sc rip tio n C R PR PR
Up stre a m p a rt
Do wnstre a m p a rt e xc e p t urb a n a re a Urb a n a re a
To ta l c e lls num b e r
C o m p uta tio na l tim e (400s sim ula te d )
0.40 m 0.20 m 0.03 m 10335 132 m n
0.40 m 0.20 m 0.03 m 15299 200 m n
0.40 m 0.20 m 0.14 m 5549 63 m n
Fig ure 2. Sim ula te d fre e surfa c e p ro file witho ut lo c a l he a d lo ss a nd d e p ths a lo ng the a xis y = 0
Fig ure 5. PC _5-3 a nd e xp e rim e nta l ve lo c itie s fie ld s.
5. C o nc lusio ns
A la rg e -sc a le m o d e l ha s b e e n use d to sim ula te a ste a d y flo o d flo w thro ug h a sim p lifie d urb a n a re a . It ha s b e e n c o m p a re d with b o th e xp e rim e nta l d e p th a nd ve lo c ity m e a sure m e nts, a nd c la ssic a l two -d im e nsio na l m o d e l.
The la rg e -sc a le m o d e l g ive s a g o o d d e sc rip tio n o f the m a in fe a ture s o f the flo w (e xc e p t insid e the urb a n a re a ), a t a m uc h lo we r c o m p uta tio na l c o st tha n c la ssic a l m o d e ls. This illustra te s the p o ssib le o p e ra tio na l use s o f suc h m o d e ls, (i) la rg e -sc a le sim ula tio n re sults m a y b e use d to p ro vid e b o und a ry c o nd itio ns to lo c a l m o d e ls whe re the d e ta ils o f urb a n a re a s a re re p re se nte d , (ii) the sim ula tio n o f flo o d p la in fe a turing urb a nize d a re a s, b ut whe re the d e ta ils o f the flo w within the urb a n a re a s a re no t o f d ire c t inte re st.
Furthe r inve stig a tio ns a re ne e d e d to e xp re ss the c o m p o ne nts o f the lo c a l he a d -lo sse s te nso r a s func tio ns o f the g e o m e tric a l c ha ra c te ristic s o f the urb a n a re a : b uild ing s d e nsity, stre e ts wid th, d ire c tio n a nd slo p e .
6. Re fe re nc e s
C a p a rt H., Yo ung D.L., Ze c h Y.,2002, “
Vo ro no i ima g ing me tho d s fo r the me a sure me nts o f g ra nula r flo ws” . Exp e rim e nts in Fluid s, Vo l. 32, No .1, 2002, p p 121-135.
De vina A., D’ Alp a o s L., Ma ttic hio B.,2004, “ A Ne w Se t o f Eq ua tio ns fo r Ve ry Sha llo w Wa te r a nd Pa rtia lly Dry Are a s Suita b le to 2D Nume ric a l Do ma in” ’ Pro c e e d ing s Sp e c ia lly C o nfe re nc e ‘ Mo d e lling o f Flo d d Pro p a g a tio n O ve r Initia lly Dry Are a s’ Mila no , Ita ly.
G uino t V., So a re s-Fra za o S., 2006, “Flux
a nd So urc e Te rm Disc re tiza tio n in Two Dime nsio na l Sha llo w-Wa te r Mo d e ls With Po ro sity o n
Unstruc ture d G rid s” . Int.
Jo urna l.’ Num e ric a l Me tho d s in Fluid s, Vo l 50, No .3, (2006), p p 309-345.
G uino t V., 2003, “G o d uno v-typ e
He rvo ue t J.,M., Sa m ie R., Mo re a u B.,
2000, “Mo d e lling Urb a n Are a s in
Da mBre a k Flo o d Wa ve Nume ric a l Simula tio ns” , Pro c e e d ing o f the Inte rna tio na l Se m ina r a nd Wo rksho p o n Re sc ue Ba se d o n Da m b re a k Flo w Ana lysis, Se ina jo ki, Finla nd , (2000).
To ro E.F., 1997, “ Rie ma nn So lve rs a nd
