EM wth L ou Elts o olvg th Pol o th D opssl Flu Flow ou Ostls Lut Gu o Vlsu stt hs pp psts soluto o th sgul ou tgl quto o th D opssl lu low ou ostl whh uss sopt l ou lts o Lgg tp. h sgul ou tgl quto oult vlot vto ts s u pplg th t thqu o th EM wth sous stuto. h pol s u to l sst o qutos o vlutg th ots sg o tgls o sgul kls sutl pt pstto s us th t pt o th tgls volv s. s o th tho pos oput o MHD s. W tst th tho solvg th pol ptul s whh t soluto s kow. opso tw th t soluto th ul o shows hgh g o u. s ou lt tho opssl lu low l ou lts sgul ou tgl quto sgul kls.. NRODUON h ou Elt Mtho (EM) s pott ul thqu tho o gt us to solv ou vlu pols o ssts o ptl tl qutos. h ppl vtg o th EM ov oth ul thos s th lt to u th pol so o. hs popt s vtgous s t us th s o th sst th pol s u t lg to pov oputtol. o hv ths uto o so t s ss to ot quvlt ou tgl oulto o th govg qutos. Usull sgul ou tgl quto s ot. o to solv th tgl quto t tps o ou lts us. s show [] th tp o ou lts pls pott ol pplg EM us th u o th ul soluto s t th ppoto ols ought to solvg though th. th o s th-sol th ou lts usull o two tps: qultl tgul lts. ths pp w us tgul l sopt lts o Lgg tp o solvg th sgul tgl quto sultg s pplto o th t ou lt tho wth sous stuto to th th-sol pol o opssl lu low pst ostl.. HE OUNDRY NEGRL EQUON W thk tht t s ss to k shot pstto o th pol w wt to solv. W D uo st pottl oto o l opssl lu o suso vlot U pssu p st ptu th ps o ostl o kow ou ot ssu to sooth los whh quto s: F ( X Y Z ). W wt to out th ptuto th lu to o th o. h pol ws stu oth uthos too ut wth oth ul thqus v wh EM ws ppl th ou tgl oultos w ot ts o pottl utos o st uto ot ts o vlot l lk th ppoh ths pp. Usg solss vls w hv o th vlot pssu ls th ollowg ltos: ( V ) p p U P V U t so hgs o oots th thtl ol solss vls o th ptu oto s: u v w v u w u () wth ou oto: Muspt v D 8. Lut Gu s wth th Uvst o ov Fult o Egg Mgt o hologl sts D.. v (pho:454; : 45-79; -l: lugu@ hotl.o). o Vlsu s wth th Uvst o ov Fult o Mthts. u ( v w ) o () wh v psts th ptuto vlot N: 978-988-7-7-5 ME 9
gf. gf t s lso qu tht th ptuto vlot vshs t l u v w. t: h st quto sus th st o th pottl ϕ so s: uto ϕ. ϕ ϕ u v w ϕ s t s kow (s o pl[]) th utl soluto o ths quto s : ϕ () ξ ξ ξ ξ ξ wh ϕ( ) psts th pottl o h oto pou ut sou stut pot ξ (posto vto). h vlot l s gv : ξ v gϕ. (4) ξ ssltg th o wth otuous stuto o sous o th ou so o hvg ukow tst (psu to sts höl oto o ) w hv o th ptuto vlot v th tgl pstto: v ξ ( ξ ) ξ. (5) Fo ξ w gt th ptuto vlot pot o th ou: ( ) ( ) v wh.. (6) Usg th ou oto () sgul tgl quto o th ukow s ot []: {( ) ( ) ( ) } ( ) [ ] wh th sg ots th ppl vlu uh ss o th tgl. (7) Fo w ot th ou tgl quto o th opssl lu low.. OLVNG HE NGULR OUNDRY NEGRL EQUON olloto tho s us o pl [4] o solvg tgl quto (7). th ou lt ppoh us h o solvg th tgl quto (7) w us l sopt ou lts o Lgg tp. h o su s v to M pl tgls ot M th ts o th pls ot N g stut o. toug ths got ppoto (7) w ot th ollowg ou tgl quto: {( ) ( ) ( ) } ( ) [ ] M (8)... N w hv to lult osg { } two tps o tgls o wth ( s o o th tgl vts) wthout sgults. hus w hv o th tgl quto: {( ) ( ) ( ) } ( ) wh pst th sts o tgls tht o t hv sptv hv t. Fo sg th lol got th lol hvo o th ukow so o ou lt w us l sopt ou lts. h us th s s utos to ol th got th ukow uto th ppoto uto s otuous o th ou. pott lso ult stp solvg pols wth EM s th vluto o th ots o th sst th pol s u t spll s gg th vluto o th sgul os. pps [5] [6] th pst so thos to tt th tgls o sgul kls oth ss: th-sol pols. t tho tht ppl to supss ths ult th D s sts usg sutl gotl tsotos o oots o to lt th sgults. ths ppoh w lult th tgls usg lol sst o oots th ts sst. Dotg th vts (os) o tgl (9) N: 978-988-7-7-5 ME 9
th ts tgul oots ([7] [8]) w hv o to pot o th tgl th lto:. Usg th pt pstto so tsoto tht stgs togth th ut tgl th s o gv : s wth stsg lto: s () w ot th w o o tgto Fg. Fg.. Nw o o tgto uth w gt: s. Evlutg th Jo o th tsoto otg wth th o th tl tgl w hv:. Fst w tht hs ll os t o. Ng th vts o pl th vlus o th ukow uto ths os usg th ouls low w hv: s s () W wt tht wh {} {} {} {} {} {} {} s s {} {} s s s s s ( th ot pout tw ). () tgls o th ov lto th s s [9 ] wh th s o opssl lu ws so th hv th s ltl pssos gv : N: 978-988-7-7-5 ME 9
l l 5 () h o sgul tgl : wh. (4) V. EVLUNG HE NGULR NEGRL osg ow tht th tgl ot hs vt w lult th sgul tgls oug (9) usg th ollowg ltos: s s (5) wh th oth two os o th vlus o th ukow uto ths os. s th o w hv: s wh ot g opots o s Usg th t tht th t pt o s: l FP w gt th quvlt o: wh l s. (6) Dotg w uth gt: (7) ll quto (9) hs th o: wh. (8) Rtug to th glol sst o otto th pol s u to th ollowg sst o qutos: N U ~ (9) N: 978-988-7-7-5 ME 9
t solvg sst (9) w oput th vlot o th N os hoos o th ou stto o oth pot th lu o. V. ENG HE MEHOD o to tst th tho w shll th uo oto o opssl lu th ps o sph o us R t th og o th sst o oots. ths s th tgl quto (7) solv ltll. soluto o ths quto ou []. Usg th sphl oots o th ol pots so pssg th posto o pot though lto: R( s q q sq sq q k) th tho o sussv ppotos to tgt quto (7) th t soluto s ot t hs th ollowg psso: ( q q ) U q opsos tw th ltl vlus o th tst o th sph th vlus lult s o th ou lt tho (wth oput o MHD) po Fg.. h ou sh s pst 4 pl tgls hs 4 otol pots. W osv tht th lult ltl vlus o th tst v los v th u o os o th ou s ot v g t tht vlts th oput o povs th o th tho popos ths pp. tt sults hv wth o os o th ou o usg hgh o ou lts. ou os ullt o th slv Uvst o sov ss o (48) 6 pg 59-69. [6] o M. ou tgl quto thos o sols lus Joh Wl os 995. [7].. Wlk. ou Elt hqus Egg uttwoths Loo 98. [8].. lls J..F. Wol L.. ou Elt ho pplto Egg pg-vlg l984 [9] Gu L. oluto o th ou tgl Equto o th h Dsol ol uso Flow usg L ou Elts ROM Joul Vol N. 5 pg. -7. [] Dgoş L. Mov N. olutos o th ou tgl Equtos th ho o opssl Flus ll Uvstăţ uuşt (Mttă otă) XLV-997 p. -9 - - - sous tsts 5 7 9 wth EM t sol. Fg.. h sous tsts o th 4 otol pots REFERENE [] Gu L D G D M Dt Ks o ou Elts o olvg th Pol o th opssl Flu Flow ou os- opso tu Pogs o Wol ogss o Egg 8 Vol pg 97-977. [] Dgoş L. M Flulo Vol. o Glă Fluul l opsl (Flu Mhs Vol.. Gl ho h l opssl Flu) Etu Roâ uuşt 999. [] Dgoş L. Mto Mtt î oă (Mthtl Mthos os) Etu Roâ uuşt. [4] Dgoş L. Du. pplto o th ou tgl quto tho to suso low pst os wgs - t Mh 86() 99 p. 8-9. [5] Gu L. spts out th vluto o th sgults wh pplg th ou lt tho to solv pols o lu low N: 978-988-7-7-5 ME 9