Comparison of Particle Methods : SPH and MPS

Transcription

1 3 th Iteatoal LS-DYNA Uses Cofeece Sesso: Fld Stcte Iteacto Compaso of Patcle Methods : SPH ad MPS Sao Toka Toka Smlato Reseach Copoato Abstact SPH (Smoothed Patcle Hydodyamcs) mplemeted LS-DYNA has bee sed wdely vaos dstal felds as a elable ad obst patcle method. At peset SPH s cosdeed as oe of mao mecal smlato method fo compessble fld ad sold mateals. Recetly a qe patcle method called MPS (Movg Patcle Smlato) has bee developed ad stated to se fo some dstal applcato as a CFD (Comptatoal Fld Dyamcs) solve fo compessble flow. As most applcato fo fld flow dsty ae compessble, MPS may have a potetal ablty to teat sch poblems effcetly tha SPH. Both methods have commo chaactestcs that patcles ae sed to dscetze cotm doma to be solved. Howeve, as the mecal pocedes to solve the goveg eqato ae vey dffeet, each mecal smlato method has both heet advatages ad dsadvatages. Ths pape demostates the compaso of SPH ad MPS fo some egeeg poblems ad teds to eveal the dffeece of these two methods. Compaso of mecal smlato techqes shold be vey sefl fo fthe destadg abot mltphyscs capablty of LS-DYNA eve fo epet LS-DYNA ses. Sface teso model, tblece model, teatmet of Newtoa ad No-Newtoa fld, coplg wth stctes ad othe seveal topcs ae dscssed. I addto a FSI (Fld Stcte Iteacto) poblem sg MPS softwae ad LS-DYNA s demostated the pesetato. I ths FSI poblem a vehcle s washed away by a tsam ad cashes agast a gd wall. Pesse of tsam o the sface of the vehcle s compted by MPS softwae ad the defomato of the ato body s calclated by LS-DYNA. Itodcto SPH LS-DYNA s vey sefl capablty to model flds. Howeve t may ot be stable fo compessble o ealy compessble flds as SPH s fomlated fo compessble fld dyamcs. Meawhle aothe patcle method fo compessble fld dyamcs called MPS has bee developed[]. Fomely MPS was the abbevato of Movg Patcle Sem-mplct method, bt cetly Movg Patcle Smlato method as flly eplct veso of the solve has also bee developed. Oe of mao dffeece of compessble ad compessble fld solves s tme step sze. Fo eample tme step szes of SPH LS-DYNA ad MPS ae gve as follows; t t SPH MPS l c l ma compessble () compessble () -

2 Sesso: Fld Stcte Iteacto 3 th Iteatoal LS-DYNA Uses Cofeece whee, ; Coat mbe, l ; chaactestc legth, l ; the dstace of patcles, c ; sod speed ad ma ; mamm flow velocty. Geeally sce c >> ma, t MPS s typcally to tmes lage tha t SPH. So MPS has potetal ablty to solve compessble flow poblem vey effcetly. I addto MPS has may feates eqed to teat CFD poblem accately. At peset a CFD softwae "Patclewoks" has bee developed based o MPS method[]. I ths pesetato mao dffeeces betwee SPH ad MPS ae show. Althogh Patclewoks has a capablty to compte FSI poblem, stctes ca be teated as oly gd body. So weak (oeway) coplg pocede to estmate the damage of stcte sg Patclewoks ad LS-DYNA s also demostated. MPS Method Otle The goveg eqatos fo compessble flow ae the cotty ad the Nave-Stokes eqatos, D Dt D P Dt g (3) (4) whee, ; desty, ; velocty, P ; pesse, ; dffso coeffcet, ad g ; gavty. MPS defes the keel fcto as, e w( ) ( ) ( ) e e (5) - Fg. MPS keel fcto A patcle teacts oly wth sodg patcles wth the ads e. Patcle mbe desty s defed sg the keel fcto, w Mathematcal opeatos actg o abtay scala ad vecto at patcle ae defed as the patcle teacto appomato model as follows: (6)

3 3 th Iteatoal LS-DYNA Uses Cofeece Sesso: Fld Stcte Iteacto -3 whee, d ; spatal dmeso ( o 3), ; tal patcle mbe desty, ad ; coecto coeffcet. The goveg eqato Eq.4 s dscetzed sg Eq,7 ad solved de the codto Eq.3 wth a sem-mplct algothm smla to the covetoal Smplfed MAC method. O the othe had SPH has the keel fcto as follows, (8) Fg. Keel fctos We eed the dsctzato fom of gadp to solve the goveg eqato. I SPH fomlato spatal dstbto of P s appomated fst. Ad gadp s defed as follows, (9) () whee, m ad ae mass ad desty of patcle espectvely. I the MPS pocede gadp s obtaed fom Eq.7a dectly, w d w d w d gadet model (7a) dvegece model (7b) Laplaca model (7c) fo fo fo h C h w , MPS SPH N N h w P P m P h w P m P,,

4 Sesso: Fld Stcte Iteacto 3 th Iteatoal LS-DYNA Uses Cofeece P d N P P w, h () Eqato volves gadet of w, whle Eq. does ot. Ths meas that MPS ca adopt o dffeetable keel fcto (Fg.). The fom of Eq.5 ca pevet dplcato of patcles ad t cotbtes to mecal stablty. Modelg of Iflece of Wall Sce MPS s compessble, flece of the wall to the patcle ea the wall shold be clded the teacto model Eq.7,.e., pesse gadet cased by the wall fo patcle s defed as follows, P wall P Z wall d P w w w whee, w ; dstace betwee patcle ad the wall, ad Z ; wall weght fcto. Z( w ) s calclated po to stat of aalyss sg wall dstace fcto show Fg.3. () Fg.3 Wall dstace fcto of a cylde Fge 4 s a smple cylde flow poblem to epla the effect of the wall. MPS model shows od shape at the fot of the flow, wheeas SPH shows flat shape as SPH does ot cota ay wall flece fcto. I othe wods behavo of Newtoa vscos fld ca be modeled sg wall dstace fcto MPS. Smmay of these two smlatos ae show Table. To clde pesse fom the wall SPH aalyss, "psh-" aalyss s ecessay as show Fg.5. I ths case SPH ca fom od shape smla to MPS. Table method # of patcles CPU tme t # of steps CPU tme/step MPS 6,5 h6m4.5s 5.E-5 4,9.39s SPH 6,55 h3m7s.e-7,83,435.3s -4

5 3 th Iteatoal LS-DYNA Uses Cofeece Sesso: Fld Stcte Iteacto MPS model SPH model Fg.4 Cylde flow poblem wth costat flow velocty Fg.5 "psh-" aalyss to smlate Newtoa vscos flow SPH Sface Teso Sface teso s cosdeed Patclewoks sg Cotm Sface Foce (CSF) model. CSF s commoly sed techqe may covetoal mesh based CFD codes. The goveg eqato cldg sface teso tem ca be wtte as, D P Dt g () whee, ; costat, ; cvate, ; delta fcto to lmt foce actg o the sface patcle oly, ad ; omal vecto of sface. CSF model adds sface teso foce popotoal to cvate o the patcle o the fee sface. MPS calclates cvate sg patcle mbe destes as follows, cos, e st st whee, e ; flece ads, st ; patcle mbe desty of flat sface, ad st ; patcle mbe desty of cove sface. CSF model mage MPS s show Fg6. If st = st, cvate becomes to zeo. (3) -5

6 Sesso: Fld Stcte Iteacto 3 th Iteatoal LS-DYNA Uses Cofeece e Fg.6 Sface teso model MPS Fge 7 shows shape chage of small wate cbe wth CSF defto zeo gavty space. The shape chages betwee cbe ad sphee peodcally.. sec..4 sec..8 sec.. sec..6 sec.. sec..4 sec..8 sec..3 sec..36 sec..4 sec..44 sec. Fg.7 Shape chage cased by CSF model of mm mm mm wate cbe Fge 8 s a wate splay o a flat plate sg SPH ad MPS. Aggegato of patcles ca be see MPS case becase of sface teso effect, wheeas patcles scatte o the sface SPH case. If behavo of wate o wdsheld o ato body s smlated, sface teso model may be ecessay to get ealstc eslts. -6

7 3 th Iteatoal LS-DYNA Uses Cofeece Sesso: Fld Stcte Iteacto MPS SPH. sec.. sec..3 sec. Fg.8 Wate splay o flat plate Tblece Model Tblece model s eqed to cosde the effect of chaotc local flow smalle tha model esolto. LES (Lage-eddy smlato) s oe of stadad mecal pocede to teat tblece CFD commty ad s mplemeted Patclewoks. Tblece effect may flece global flow behavo some applcato. Gea ol flow poblem was solved to vestgate the effect of tblece model. Fge 9 shows the eslts of the aalyses sg MPS wth ad wthot LES. Patclewoks has a capablty to cot the mbe of patcles specfed ego. So a bo ego was defed fot of the gea ad the chage of the mbe of patcles the bo was compaed fo two cases as show Fg.. Clealy the case wth LES moves p moe ol tha the case wthot LES. As SPH LS-DYNA has o tblece model, smla aalyss may estmate the qatty of moved-p ol fewe tha eal. (a) LES off (b) LES o Fg.9 Gea ol flow smlato sg MPS -7

8 Sesso: Fld Stcte Iteacto 3 th Iteatoal LS-DYNA Uses Cofeece Bo defto to cot the mbe of patcles Fg. Nmbe of patcles hstoy Applcato Eample sg MPS ad LS-DYNA Patclewoks ca compte FSI poblem. Bt stctes that teact wth fld ae teated as oly gd body. FSI sg LS-DYNA s also possble bt vey tme cosmg. Combato of MPS ad LS-DYNA may be a pactcal solto to model FSI poblem. Oe of the applcato eample sg MPS ad LS-DYNA s a tsam smlato of vehcles. The damage of the vehcle dfted by tsam shold be estmated. If passeges ca move ot fom the dfted vehcle opeg the doo, may people may svve fom the dsaste. Safe desg to potect passeges fom tsam may be possble. I ths sceao, pocede of smlato s cosdeed as follows; () Pefom tsam smlato sg MPS. I ths smlato vehcle s modeled as a gd body sg STL fomat geomety. Vehcle s costcted sg gd body patcle clste geeated gve STL geomety as show Fg.. The vehcle s washed away ad mpacts wth a gd wall. () Pesse hstoy of the vehcle s obtaed fom MPS smlato. Pesse s calclated o each gd patcle ad t s mapped o the STL vetees. (3) Pesse at the patcles o the sface of the vehcle s coveted as pesse hstoy load data actg o each fte elemet. The patcle closest fom a shell elemet s seached. (4) Eecte cash smlato of the vehcle agast the gd wall. The vehcle s pshed towad the gd wall by the pesse load. I the MPS tsam smlato, the flow of the tsam ad the behavo of the vehcle ae obtaed as show Fg.. A vehcle s placed at the posto of, mm fom a gd wall at the begg of the smlato. Wate comes the model fom the flow wth the velocty 4, mm/s. The vehcle ae washed away ad cashes to the wall. -8

9 3 th Iteatoal LS-DYNA Uses Cofeece Sesso: Fld Stcte Iteacto Fg. STL vehcle geomety ad geeated gd patcle of vehcle fo MPS smlato flow t=.5 sec..5 sec..75 sec..95 sec. Fg. Reslt of tsam smlato sg MPS The evet teval was.35 secods. I ths smlato pesse hstoy actg o the sface of the vehcle was obtaed. The pesse was calclated o each patcle dg the smlato ad the t was mapped o the STL vetees by post pocessg. Afte the tsam smlato, pesse hstoy was coveted to pesse load fo LS-DYNA cash smlato. I the mappg pocess the pesse at the closest gd patcle to a shell elemet cete was appled o the elemet sface as a pesse load. Fge 3 shows the mappg pocess of pesse dstbto thogh patcles to fte elemets. I the secod stage, taset aalyss of the vehcle model[4] sg LS-DYNA was eected. Thogh the smlato, defomato ad stess dstbto was obtaed. Fge 4 shows the defomed geomety ad Mses stess dstbto of the vehcle. Lage defomato ca be see ot oly the ght had sde of the vehcle whee the vehcle cotacts wth the gd wall, bt also the left had sde. pesse (KPa) Patcles STL vetees FEM shell elemets Fg.3 Eample of mappg eslt of pesse dstbto at tme =.85 sec. -9

10 Sesso: Fld Stcte Iteacto 3 th Iteatoal LS-DYNA Uses Cofeece Mses stess (MPa) ght vew (wall sde) left vew (tsam sde) Fg.4 Defomato ad Mses stess dstbto of the vehcle at. secod. Coclsos Oe of patcle method MPS fo compessble flow was todced ad compaed wth SPH fo compessble flow. These eamples showed that MPS had pactcal capabltes,.e., sface teso model ad tblece model ad so o. I addto oe way coplg pocede sg MPS ad L-DYNA fo FSI poblem was also eplaed the pape. Refeeces [] S. Koshzka ad Y. Oka: Movg-Patcle Sem-Implct Method fo Fagmetato of Icompessble Fld, Nclea Scece ad Egeeg, Vol.3, pp.4-434, 996. [] [3] Sao Toka ad Takm Kasahaa, Smlato Techqe to Estmate Damages of Ato Body Washed Away by Floodg, COMPSAFE 4 [4] FHWA/NHTSA Natoal Cash Aalyss Cete, -