石 康 浩 Overview of Diverse Computer Simulations and their
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石 康 浩 Overview of Diverse Computer Simulations and their
ῒΐ /, (,**1) . ,,+ῌ,-3 ,**1 + . ,**1 1 +2 Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE῍ This paper presents an overview of diverse computer simulations, such as those based on the finite di#erence method, lattice Boltzmann method and molecular dynamics, to discuss their potential contribution to volcanology. The general features of several numerical methods are described to provide information for finding appropriate approaches to investigate various volcanic processes on a wide range of time and space scales. This paper also outlines previous numerical studies of some volcanic phenomena, including the generation of magma deep underground, the ground deformation due to magma injection into the Earth’s crust, and the evolution of giant eruption columns penetrating into the stratosphere. Fundamental issues on conducting computer simulations of volcanic phenomena are then discussed with the aim of promoting e#ective numerical studies in volcanology. Key words : simulation, numerical procedure, modeling, multiphysics +ῌ ῐ ῎ ῑ ῏ LMl4|N}@o7O:Y"'67 P(~I{2A% QR(S !"#$% &' (T ,**/ ; LMUV+_W ()(*+',-./'012 +33/a ; The Earth Simulator Center, ,**/ B 345%6789:;<=>%$?:@2A XYZ% %B CDE2FG HIJ 8Z[W} \8]L4I2 KL2MNOPQR0'S TUVW8 AoB z'$?:^<_`Z%o{ 67 A%B X !"'#Y"<$7Z%0%12 LM'!a:9'671b2 &[\:@2FG H GcRx:~I%$?:@ ''()] *^+_(*A2)^T^'`,<- 2A%B d _ ef¡,'_ e¢( Z%.a:bcde4 /f?'0gh(< £gh67S T¤8 671)^+¥_ 2ij'12k3<l4Z%56_bcdm87 '67+o ¦iUV1 nKo% 8T9 +33- ; : ,**- ; ;< ,**+ B §¨-0'S © 1A?uvª« ,**+ e p= >?:qG @AB:Y"<r:C"12 29oB 4 ,**. m8 ¬~I jU"k\UI:f' ®KIo d l: ,**. ; Hidaka e s8 Dt:#uvwbExJ?Y" et al., ,**/ B 6m_n'_67opq¯ghr°6 yA2VFG:[:G H( 7 ¦s '±²³´«b© ,**,ῌ,**0 t 8V :IJK4I%$?:@oB z'o{ zIm8 9'67e4L7+'+<K2 µu:vG¶ ·-*/ῌ***0 ¸w¹y+º5»x -ῌ+ y¼_ e67z National Research Institute for Earth Science and Disaster Prevention -ῌ+ Tennodai, Tsukuba, Ibaraki -*/ῌ***0, Japan. 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(g* £ v 9¤¥3'¦ a ' BN( ,'-9 a|^D ilN(S,lG :+9(D-/9¬ B HI GG"2C'}N_~ 2CpNif3:aG (+33/b, c) 1"`V*=/3' upN9¬g f3" H:+jk, ,ῌ. ῑῌῒ῎ῐ "-M®¯x §Ph £°c±²C AB C Finite Element Method L-9 f3D3''2' ¨ FEM! ,V* a, G3 3LlaG ailJK,³©-F BN( GbZ<'M/3' B E Oe=/- AB~ C Finite Volume Method F9 VW,cn+ ! ( L-9 FVM! 3,laG , 9 +d B~ 9 ´HIµ¶² + - 9defe((g yO! ,f3 ,aG p h +b! G3l +dei N,ª« · 1,¬*¸¹~ Vo j=, ()klm&P3noaG f sW", p+.,'0 !HIG,?-'01 qe pnoaTrD sWWggG'l1" " ¨ ῏ ῑ fv · dS fdVª« ῒῌ῎ ¨t ῐ῍῎ (/) G¡3N(S - dV 9~® dS 9º ¼¸2¹S ºPQ G»OLEJKLMEJNO 227 G TU" 7h Vo Vo P< F!<QI" So (/) l {UE);/ 7m, ! f " (/) A5@" OLEJKLMEJNO (.) #$%!&'( " , 3XIZ" ? (/) )*+ l f=:VPQ A5g Xql !!,-./ 0"1# $%" )2 &" `F!c fEO= A5g )" 3 456'(7) F 8" 3 95 *+, F!c= G*; -.:3";/01< =>?)2 =q!+A5" l b;G ' 3 rse fGravitational Many-body problems ; N rs *+@34A5 BCDEFG6, (g xmQ #Grs!d *+" 3+78H!I OLEl)" > JKLMEJNOI(9:;< (G ^m F! (Ebisuzaki PQ 95 =R'>=R>?S et al., +33+) b hO O¡ He G¢ @TA! JKLMEJNO( BC (/) <£%¤ f¥ +332g FJKLMEJNO D"UEF VWG ! 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(Particle Element Method : PEM) ,FwJ ,)GH*, - ,:;, ( J xyz8aB.8'(E 3 ! )*+<#=>?@AB$ >! 4[ 8C%DE&'8' F#=>?@A( 5t0{6 Ht0 |xDYk 50+ 8)GH*IJ)*+ Ht0+, F0& })J , K+ ,- 5t09~JYX+m~ !"#.- !"# /#=>?@A KL [- KZV+,( 0+1/MNOH*)*+ F0 }Z@ F - & 3 !)*2 34 , 56780 +E wJ ] ,)P8( )*8' 3 3 ! QR 9S+,:;T !)*80., 4@A#6 2| UVW 4Hard Particle Model 50 Hard Sphere \A .wJ J,o Model6 , QR :0,+<=UVW 4Soft (,Mt'(E J ] Particle Model 50 Soft Sphere Model6 , >? M$H*IJ)*8' MJ ]$ T UVW + 0 + 8MXY( +,(Z@*2 A ,Z@Y[ \ABCDY(])* !#n@A#,:; )* +E^_ 1+ <=UVW < DY9+, . F1,8'([])*+ +0&d 8M8 ¡ E^_,( +_` GCa J J JJIJ 9 HbBCI2(J)*+0&12 9 .[t'J J¢8 de 0UVW <=UVW 8cK Y(E( [)GH* +de%fg, Lh- !" )*+A! £¤!n@A#, #*Y 4M +3316 3 !N :; OP( 3 !,|' OPQ i (+332) i (+332) 67 BZg¥+¦§,8 ,ῌ++ SPH !"# J )*$jR &'( FNS SPH 4Smoothed ' J, 8'(qJ -i¨ D ,**, ,+ © - ª ,ῌ+- Particle Hydrodynamics 6 SPH k= «¬W®# ¯W°!£®£#,:; lTLUCVD 4mn>V*( bUVWMX80J )* ¯W°! 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(,**/) _ Niimura (,***) =bx M1<bL=^ <>7©v= ª1q0«#=< ;yc!Jdz{kῌhs0ih!Jd y| J<bL<K=m~ 7 FMNOP0MQ@Fe5(!= aB 2 }! ¡¬ 3,ῌ- `4 #= a% <Q 23G}G6_ bx fm~ <h®0I ¢S£T& 2==g<>w(! !( (!= 3Aharonov et al., +331 ; Iwamori, +332 ; Spiegel- I) K=hijFk VOF 3Volume man et al., ,**+ <>4 !( Niq<¯¤ Of Fluid ; Hirt and Nichols, +32+4 _Prus m~ °±M0)² =B@³¥3 (Sussman et al., +33.) <>56,@= ´¦µ¶)+!= =D) CSF 3Continuum -ῌ- %&'()* Surface Force ; Brackbill et al., +33,4 aFl(! avU¦:(// § = K=!mnA;o ¨<(~©¡ : @F^ \H ·q=v~_&78(!= N (+33/e) pdq<r ¸F`}/a%ª£i+F sWt (,**-) [ P{O0= /U¦`}i«%B+ ¬: ul%=^ Journal of Computa- ( 230 C ¹ » ¼ " # 8s -9 Mti] l'v1) \? f GABCDEAFG 8,ῌ+. -9 u.//a v wxo_4'/jz 23\?t !" #$% yM 4zLH!23 & ' ()* 1 Eo {m|:o )+,-.! /" #)0$ % _;<}&E 0~P)Q &1 234')*( )5/*6 zh/3Z 23 7+, 8,ῌ- -9 ). Kuritani (,**.) :;</ Z~P2 4'* 4m% 1 0+=>1/2?& 2 -ῌ/ ab o_`o0 /k:o @ +34&ABCDEAFG 8,ῌ3 -9 ). _+ Y 8, BEOP#9 Eo *(H! 8I5'6J +331 :9 K E L78)MN / #GOPQ&9/ qT+ 3/qT :R ;<)= STOUVWTXYO Z1/Hf )>Z[\? 8,ῌ3 -9 2@A ;<: H! (Iitaka et al. ,**.) J-i 1oJ`^ o_` 1 o_` *67+, 8,ῌ- -9 -ῌ. ABCDEAFG0)5 # B]^CD `ABCDEAFG m< 2 M , E_ FGH`<)Ia +% Z@ jz \? 8L JK LFbM/0c FV +** V|9 )` 234'*( *6&9, 8,ῌ. - ; dN' Q)4 ` Y B¡¢T OP ,**/9 ef&9, 8,ῌ0 - ; Dahm, ,*** ; Mériaux *) /)< / 1 8s .9 and Lister, ,**,9 Q. L `<R 3Z@ +:wAE{/)}7 Sg Th*( *6&9, `B]b| (Ryan, +322 ; Saunders, ,**/) ef&9, (Cayol and ) jz ¡£¤¢)5jkP\? Cornet, +331 ; Gudmundsson and Brenner, ,**/) U. {Y¥1 )5 # i.! /2V £¤{Y¥ ) i 8o_q T/Mivi19 =>o_Mt¥¦ # L!WX9:Y% ¦§:) §¨P23/ ¨ jk$a I. l4mZ[\i © !" o_©@ªª«P¬E2M l)#n /i]/(^ 1 (Carroll iª«¬) mg ¥4M® and Holloway, +33. ; Tait et al., +323) o_`op JKbh /323Z®¥V¯T) ab (^qT %¯w4 /)°s +" #r)s /0c q °± ;</ Wohletz et al. (+32.) 2± T+. tc +du . +qT P o_3/qT+m +e%HfTgh iv Y ² |²)Q m³¤ ³I ^LY^wExy/3jz pT{ .)5jk !" Z3´1X¡¥ YP`o . i]kjLL GP 8,ῌ+, -9 1 P)bS l)m% / )n|Eo 4' 8}~ µ;<0 bT 8Clarke et al., ,**, ; GEAFG9 g n| Neri and Dobran, +33. ; Valentine and Wohletz, +323 qT+//oJ`^ ab :9 0 `¥4´+b `o1 ¶`µ `µ¶_/·u 4' b]4'@ Kinjo et al. (+333) =p ' q Mi2a}-i 1oo/ (,**/) : Lennard-Jones SGAP)r+3 G¸M +¹{º·¸/ 4&ABCDEAFG 8,ῌ3 -9 ))5$a ~`º»InWfg6G)¼B¢>@Q<=>?@<AB 231 Oberhuber et al. (+332) Dartevelle et al. (,**.) ! "#$ %&'( (,**0) ) * +,-. /01 234 5678 9,ῌ. :; <=>?@<AB (% (+33.) C)D/E61 FGC23HIJ%KL30MNO P56QRS T U.VW.XYZ@[ \]^ _\`K56Hab ! c d6CeRBfg3061 h"# i$ Uj%k3T&l)mn'(o)3 p -1 'JKy<=>?@<ABC6L4³ OP 9´µMN¡>;1 , ³'¶·bO PC6L4³NOP/ QR S5T0UVlHS5¸0I¹§ 3 Lv)2306G¨3061 Fig. -. An example of Molecular Dynamics Simulation for bubble nucleation (Courtesy of T. Kinjo). The time evolution of bubble nucleation due to instantaneous expansion was investigated numerically. A bubble with several solute molecules (red) appeared in the surrounding solvent molecules (white). qrs)t*+ ,u56v0)w-03 06/I01 xy -0zg6. {. 3 |}D/-~I.E^ 0)v.Ms156I2zg306 (Armienti et al., +322 ; He#ter and Stunder, +33- ; Tanaka, +33.)1 QRSOPT 34-fg3065 6756 9Hurst and Turner +333 ; 89 +331;1 5) '(:0T GI;5 6 E6v05z G<= BQ@ (Volcanic Ash Advisory CenterVAAC) v0 }[@Ifg hI.<=>?@ <ABM=>3061 .1 H<=>?@<AB 9 ? @¡>;1 ¢£¤¥ +33+ AvB E6C 2 ¦ kgῌs §D OPHi$E#¨/ ©ª +.** F«G§H¬I'D 9§ H®ῌ§H¯®; qr3°'±3E61 Fig. .. An example of numerical simulations of a volcanic eruption column accompanying a horizontally spreading umbrella cloud (Courtesy of Y. J. Suzuki). The calculation was carried out with the discharge rate of 2.*²+*2 kg/s, which is comparable to that of the Pinatubo +33+ eruption. A vertical cross-section of the mass fraction of the discharged gas-particle mixture at +.** s is depicted. ¡ » ¼ ¼ 232 = v B # ῌ " R z A (Gri$ths, ,*** ; ΐ Manga and Ventura, ,**/)$ z"!ῌ9=v !"#$ ΐ%& '( (,**,) ) Seino et al. A#xy2 G '2 )#9 (,**.) ,*** * !+"# |B0^[0C: W ,῎-./0#$ 1( (+333) p# (Hon et al., +33. ; Kilburn, ,**.)$ 2 3῍4#56 VUW2 VSῌA# 7#8 !"#9$:;<= ^2 H=fMqVJ2< #%#$ -ῌ0 Wp#$ &74Q ῌ9=vA# ,|}2,tuB8 z=va &>?'2 2()*+ 2<aB9^[_J"#$ YB ῏+ @ABCD ,῏EF GHIJ"# abW,G[!"# '/ K-#$ L.B/0 E1M2 !) 0 ῌ",)B^ 3(4A#N567 28OP9A `KA# , #$ #Q,#$ :;<B xyΐ'2 Y)J @,ῌ- XF J2Y P9A#=RB῏+ @STF IUV0 J @,ῌ/ XF , Wp#$ z"! , 2WRB$ 2 #5M4 +! STXY>?2 Z@ABHB , =+"#$ 2 /Wῌ" !Cῑ/P9A#DEP9[BF0 +)R%#P9<B-M, ' !G[!"\] @Minakami, +3., B^F H @ r¡¢£¤F Wp#$ Q2 1W2IJW_;`KA#abcdefg+ ¥ῌ)¦ῑ§Oz,A#{|Lῐ "# (Mastin, ,**+)$ =RB῏+h0 ῑ<B @¨v©£¤F Wp#$ =RL%!"# ijbklMm 4QBV 2 ¡ª( (+32.) Miyamoto and Sasaki (+332) Young ῏+22nNOPQoWR# and Wadge (+33*) B^p#$ « 2 ¢+7 4QBRS2JGT+"B4QWp#$ z,*+Qx£1¤¥ qUrcrsRBA# itu £5M ' @Costa and Macedonio, vMm J2 iVSWm w&"#=vR ,**/ ; ¬( +33*F$ z ¦ S<Bxy !"B$ z4QBSTB^ (Favalli et al. ,**/) ) ®¯jrjJ @,ῌ+- XF ῏+IUV02 SPH J @,ῌ++ XF OG[ΐ (Crisci et al., +333) p#$ H1W2 RSY{Wp#$ ΐ%& Z[( VSῌT§ !(°,ῌ"B#ab® (,**/) \4S]>A# ^[_G - ) g+"# CῑZ@A{|OP^[ @Hidaka et al., ,**/ ; ¨ /F$ _8& YB`ab!"#}c+"#$ B&ῌ".#VQE !±# -ῌ1 VSῌ X*W©ªA#«¡ῌ eῌ2 rcrde+"BJJTfA# VSῌ ²¬A#hD#$ 8 RS BT~]ῌ".#$ VSῌW2gh -M, ῒ¤E'$ n ®³B {|=R iῌ<BP92jk+"#$ 8 =RBRS´O+:#µ¶ELῐ ;<= lG[B+"D YJ @,ῌ/ XF '²¬ Wp#$ #m2 VSῌnYBo#p n~Wp#$ zE2 ¯°)±B^ *· ^2 -h<W+%WqVW 64#&ῌ" Wp#$ 8 z" R#rsB$ !VJ8#²¸ p# (Denlinger VSῌtuWp#H=6 2 ) vwxyVSgh=Rz,A and Iverson, ,**+ ; Takahashi, ,**+)$ Beven(,**+) ³ ( (+323) B^²´µ¶ ·LB#$ #zWp#$ z8 VSj){U|}B^ -ῌ2 VSῌn~<BBA#$ & g «¡ῌA#xyW2 XW¸¹¥£5 hz,yVSῌῌ9nh=Rz, MY)J @,ῌ- XF W,ΐ' vvVS VS TUVSQ8 @Laigle and Coussot, +331 ; º¹(¬ ,*** ; Z»(º R9® »³§"C¬^¼[\YZ[2\Y]^ 233 AWXoIpRS?&TUYZ[ 2\Y]^N> VVO +31/ ; Nomanbhoy and Satake, +33/ ; Tinti et al., +333 qr0 R9:R s t u;=vw&YZ[2\Y]^ Ml VxW ,**+ I 9X AyTUY=" zN VZ{ ,**. >5 -ῌ3 ῌ῍῎ R| AWXBC }~VX<. ;u[07'05 !R9AB <.I\ AB+,D X]^ M_R|`ab;R9HI~ / A YZ[2\Y]^ VOµ c 9 -. R¶= ,** m-ῌs 0A ¡&¢iN0 <£ · -I¸¤ ¤¥¥8¹¦2º .®D &Cn£7 Fig. /. An example of lava flow simulations (Courtesy of E. Fujita). The lava is assumed to flow from a vent on the southeastern flank of Mt. Fuji with a rate of ,** m-/s. The lava spreads towards Gotenba Station under the influence of topographic heterogeneity. Cce=& \]^ ='" H"05 u056>7'de Q? R| S?fr ghstN i j=`kJKm* N R| = (lm* ]^ X]^ X8Q?> !e=/\ ; _n (granular flow ; Duran ,**, ; Jaeger et al., +330) 05 :oghp X]^ \]^ Vi# -./h q =rst0& uv (Branney +32. and Kokelaar, ,**,) \ 7'= wx C-./h" !" #$% 2 X \ y^8 += &'()! &*+ ,-. , X8 m; /0 &1 0!23/ 4 05 6 4 7 R| \ z{YZ[2\Y]^q>m; Neri /\E05 (Dobran !"#8$9 et al., +33. ; Giordano and Dobran, +33. ; Todesco et al., :%&'&(7');6) ,**,) | 3HR9}~ 8 < =>* ?@ !AB H¡¢&N 7(<R| \ C+,-./D&EFGH01 £ 4 ¤¥¦_&= §X¨ 2I JK L3M0456NOO C©=ª \ R 7 !P825 6Q? | \=bS&¨«N Ishimine (,**/) I¬F^ n 2HR90 R9:R; <S=I<>0?TU@9A :R ® MlN Córdoba (,**/) 5 VAWX > YZ[2\Y]^J_ ¯N0 BC 4U BC `D" (Heinrich et al., ,**+ ; , ° z{-./0 X]^:%& Kelfoun and Druitt, ,**/ ; Pitman et al., ,**-) NX K05 VItoh et al., ,*** ; u±n\ +331 BC 0 abIEF0cd"44; -./No²0 >5 (Wadge et al., = >N", AWX0e=f'4 +332) n9O (+33.) 0 X \ e= gGQ?H0-./h? l*zN-./ | T ON AWX9i4 !B f014 \]^ e=(7 OO;e=& "IJ jK '5O Ok70! 1$D V,ῌ+* L 7'k7&Ml>m* 6 \> 4Y^E//\¬\^-./ VCampbell et al., +33/ ; NOnPQ +33* VR|³´/\ D; 8 » ¼ 234 {GAwuwqOqy |U#I( Malin and Sheridan, +32, ; +33- ! ,ῌ+* "# $ . " (Mitani et al., ,**.) SPH ,ῌ++ _`QOPQROS) }~ TU3 " (Nagasawa and Kuwahara, +33-) %&'( >4%AqOb#I-)F -ῌ+* >'( - GWH^a2 TU) ) *+*, ' PQROS0"Iz>FG84(A^ O ( - ./%"#) *+*0 123' |'%Z %W-d"#I( ?01 43 0 523!6# 17" Aj'! .%& /'3#v%J< -8- 9#:$%; ! &<'=!>3( QAc '; 3b/e%w "?0@!)3*+A%& B *+* 4R3"#I'( ">" -F) 0,--."##:C"2%/ 9*+*D a&%G8& 2W3 %I( #:$%; %&0' 012 OPQROS ¡X&)U'% ¢3'W +332 ; White et al., ,**-( ?!0 363!4 }~ F%£00¤¥'( TU3_ >"# 5%/./%' E `QOPQROS3¦"#I23 67 ,**-( ">" -F G8) H!C" ) a2 §$¨"#I>%]c%F%I( I9:I 0;%J<K=>L%J<M? Gm u> §) _`QOPQROS N@A%& OPQROSTU) 3GW©TU W0'3%II/- 'VWAXI%I( '( fd Mo' 9; 3 V ) B3YZI#CDG8 E ªOPQROSo« 0¬#%I [%FJ<ATU\]GWH^0 _ I/0 - Gm'3d"#I( TU `Q )a\]3VF%I( bc 3gI#) Y'%TU37b# i! Idef 3gI#) H !JhK!LGi R%& z[ f!?f ®Hf3 3YZ2jMklmn NO%&3o"# P[ YZ2 F3)E Q¯ V QRpST% G"#_`QO W%ITUA#12"%]c%F%I( PQROSAU0V2Q#I (Epstein - Gx3A OPQROSTU3P° and Axtell, +333)( ).%>6qr ±2450%II/m)"cF2>²%I( s _`Q%/WI#XJ'3 OPQROS)!b G0 G85YAZ ! t!'uvwxy z[{ Iq³F#I( _`QK=) 'F |%& }\ '~3]A^ ' ´e%!Z 3µ6'%HF"#I 3_`AZ %&IOPQROSaI( ( a ./%Ez ¡¢£7!!b¤¥ !bo" ) #W co"$] 0 & ./%¶ 0& ; L%/A #_`QH dA e%Oqy (GIS : >3I#¦:)%§ROPQROS Geographic Information System) "TU ¤¨\©IªX a {|3YZIe% aI( bc bE P fg&h! ij «3!b#Fb ·¬"#I#0©¸ "3.k' (lm)[AOPQR )%I( - ./%·¬OPQROS Gm OS%&0AF#I efnTU % k¶)"2>4I( !befK=TUo ,**0( f @,3g ¹z"./3 %/AG8 ]TU OPQROS *pb+ a2)®'%¯°0º G8a 0#± I0I2>'( bc Aspinall et al. (,**0) ) '( a ) :8f!M»²f% qrR! ,(-%& z[I & )³´"#I%Ia2 ¯µ%m0/ # st;~ G" uv%R_ ( ¶#4&%OPQROSK `Aw"#I( Guidazzoli et al. (,**0) =)·x3A40aI)Ib aF ) OPQROS {|xyf'%TUN| %W¸ ¡X&) a VV)G # yzs*Ez384b 83¹4%I( ¯q'~3º¼"J 4abe»£¼¼12'»#%I!"#$%!&' 235 t8x` EV54!"#$% !&'yzc{.2T 4ab !"#$%!&'()*+ , |?.+ .`V*< -.!"#$%!&'/012 J* 3 4*5 678() + 49:6;!"#$%!&'* ῏ < ^3ab}~ ab!o 44* =*>212 ?.+ !"#$%!&' 4 ῎ ! 6s/ab}^! "#$%!&'PQ (<E E 4!"#$% 4&@A*BC?. ^3ab}~ *siab > 3 DE2FGH% 4 "}*ss k I =*'( )?.*< m%|%I!y\ ¡pt# !"#$%!&' >2JC $ 32¢2%.8t *+K >L%I,M b£¤(<E 6s/ab}¥ DE2?.-.* 8/NO ¦ ^ 3§R 8PQR>0*<;S1 ¨5(<E H* 2+ 3T8PQ3;> 45M *skab}©>ªh*s6ab ;* 6.+ 789<:; } ;>«l;7 ¬;®* )2U> ?T 4!"#$%!&' ?.*<E ?2>$ ;;2 V< ¯ E b 6s/ab} WT=. X4Y */¡3 °4&..46,abijkl ZI[\>*<!"#$%!&'/M mn± ²³%´ °4µ¢fª46¶& ;5&].?@NO !"#$%!&'/!|µ± 6u. 4 A5BC^_ !"#$%!&'/D !"#$%!&'E.+* E; ` !"#$%!&' {£¤¥¦ }§¨~ /F7GabHRcId RTJK5LU4abMNeOf PQ*<; Tg E hQXT !"#$%!&'RS TUabH 4,ijklmnabV opWq5 ` 44!" X rstuvsUabHwt4x yzY!"#$%!&'Z+ {An et al., ,**- ; Tanaka and Yamamoto, ,**, ; [\|T ,**0 ; ] ^|*} ,**/~ ?TF7abH] > G*+abH_54 !"#$%!&'K5Luv`a?. E2 b*=T J4!"#$% !&' *s$cdeVf ghi* jsH*+Kt8 >NU ['Fmnab*< k*<;>* labmQ: +*8 no!p* qr:2U 6s5F'*t5!"# $%!&'/*<uv+ wt ῌ ῑ ῐ ῍ Aharonov, E., Spiegelman, M. and Kelemen, P. (+331) Three-dimensional flow and reaction in porous media : implications for the Earth’s mantle and sedimentary basins. J. Geophys. Res., +*,B1, +.2,+ῌ+.2--. ©^ ' (+31/) +13, ª«(·¬`O / k , ,2 ..3ῌ.0*. An, J., Ueda, H., Matsuda, K., Hasome, H. and Iwata, M. (,**-) Simulated impacts of SO, emissions from the Miyake volcano on concentration and deposition of sulfur oxides in September and October of ,***. Atmospheric Environment, -1, -*-3ῌ-*.0. ¸)®0|¯ *° (,**-) *±¹4²+*±³ !"´º.»%m+,7 µm +/ ª$¶ spab!·p¤ ,-.ῌ,-/. ¸¹6 (+33.) +Ns *s:ºp ,.2p. Armienti, P., Macedonio, G. and Pareschi, M.T. (+322) A numerical model for simulation of tephra transport and deposition : applications to May +2, +32*, Mount St. Helens eruption. J. Geophys. Res., 3-B0, 0.0-ῌ0.10. Aspinall, W.P., Carniel, R., Jaquet, O., Woo, G. and Hincks, T. (,**0) Using hidden multi-state Markov models with multi-parameter volcanic data to provide 236 º » ¼ empirical evidence for alert level decision-support. J. Volcanol. Geotherm. Res., +/-, ++,ῌ+,.. Beven, K. J. (,**+) Rainfall-runo# modelling, the primer. Wiley, Chichester, -0*p. Brackbill, J. U., Kothe, D. B. and Zemach, C. (+33,) A continuum method for modeling surface tension. J. Comput. Phys., +**, --/ῌ-/.. Branney, M. J. and Kokelaar, P. (,**,) Pyroclastic density currents and the sedimentation of ignimbrites. Geological Society Memoir ,1, London, +/,p. Brebbia, C.A. and Dominguez J. (+33-) ῎ -2*p. Campbell, C.S., Cleary, P.W. and Hopkins, M. (+33/) Large-scale landslide simulations : global deformation, velocities and basal friction. J. Geophys. Res., +**B/, 2,01ῌ2,2-. Carroll, M.R. and Holloway, J.R. (+33.) Volatiles in magmas. Reviews in mineralogy -*, Mineralogical Society of America, Washington, D.C., /+1p. Cayol, V. and Cornet, F.H. (+331) -D mixed boundary elements for elastostatic deformation field analysis. Int. J. Rock Mech. Min. Sci., -., ,1/ῌ,21. Clarke, A.B., Neri, A., Voight, B., Macedonio, G. and Druitt, T. H. (,**,) Computational modelling of the transient dynamics of the August +331 Vulcanian explosions at Soufrie ◊re Hills Volcano, Montserrat : influence of initial conduit conditions on near-vent pyroclastic dispersal. In The eruption of Soufrie ◊re Hills Volcano, Montserrat, from +33/ to +333 (Druitt, T.H. and Kokelaar, B.P. eds), Memoir ,+, Geological Society, London, -+3ῌ-.2. Connor, J. J. and Brebbia, C.A. (+312) ! "#$%&'()* + ,-./ ,.*p. Córdoba, G. (,**/) A numerical model for the dynamics of pyroclastic flows at Galeras Volcano, Colombia. J. Volcanol. Geotherm. Res., +-3, /3ῌ1+. Costa, A. and Macedonio, G. (,**/) Numerical simulation of lava flows based on depth-averaged equations. Geophys. Res. Lett., -,, L*/-*., doi : +*.+*,3/,**.GL *,+2+1. Crisci, G.M., Di Gregorio, S., Nicoletta, F., Rongo, R. and Spataro, W. (+333) Analysing lava risk for the Etnean area : simulation by cellular automata methods. Nat. Hazards, ,*, ,+/ῌ,,3. Dahm, T. (,***) Numerical simulations of the propagation path and the arrest of fluid-filled fractures in the Earth. Geophys. J. Int., +.+, 0,-ῌ0-2. Dartevelle, S., Rose, W.I., Stix, J., Kelfoun, K. and Vallance, J.W. (,**.) Numerical modeling of geophysical granular flows : ,. computer simulations of plinian clouds and pyroclastic flows and surges. Geochem. Geophys. Geosyst., /, Q*2**.. Denlinger, R.P. and Iverson, R.M. (,**+) Flow of variably fluidized granular masses across three-dimensional terrain ,. Numerical predictions and experimental tests. J. Geophys. Res., +*0B+, //-ῌ/00. Dobran, F., Neri, A. and Todesco, M. (+33.) Assessing the pyroclastic flow hazard at Vesuvius. Nature, -01, //+ῌ //.. Duran, J. (,**,) 0123456707189 :;5 < =" > ?@AB ,3+p. Ebisuzaki, T., Makino, J. and Okumura, S.K. (+33+) Merging of two galaxies with central black holes. Nature, -/., ,+,ῌ,+.. Epstein, J. M. and Axtell, R. (+333) CDE5FGH7 IJK-LM.N OPQROS. 5 TU VWXY8 Z[\] ,-0p. Favalli, M., Pareschi, M.T., Neri, A. and Isola, I. (,**/) Forecasting lava flow paths by a stochastic approach. Geophys. Res. Lett., -,, L*--*/, doi : +*.+*,3/,**.GL *,+1+2. &%^῏ (+33.) ῌ4_`ab cde4\] E ,.2p. &fg (,**.) hijOPQROS.7kl mnopqr abs4tuv!wxyz{qr |}~ +- O.Ln 02ῌ1+. 0D4E (+332) 0OPQROS. A ,*2p. ῍8%i (,**,) hi¡¢/£¤J¥,¦§¨©no7 e ªk4E« -1 ,-ῌ-.. Giordano, G. and Dobran, F. (+33.) Computer simulations of the Tuscolano Artemisio’s second pyroclastic flow unit (Alban Hills, Latium, Italy). J. Volcanol. Geotherm. Res., 0+, 03ῌ3.. Gri$ths, R.W. (,***) The dynamics of lava flows. Annu. Rev. Fluid Mech., -,, .11ῌ/+2. Gudmundsson, A. and Brenner, S. L. (,**/) On the conditions of sheet injections and eruptions in stratovolcanoes. Bull. Volcanol., 01, 102ῌ12,. Guidazzoli, A., Diamanti, T., Ponti, F. 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