ῒΐ  /,  (,**1)
 .  ,,+ῌ,-3 ῕ ῔
   ,**1  +  .  ,**1  1  +2 Overview of Diverse Computer Simulations andtheir 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

LMl4|N}@o7O:Y"'67 

+ῌ ῐ ῎ ῑ ῏







 

 !"# $%&' ()(*+',-./'012

P(~I{2A% QR(S
(T ,**/ ; LMUV+_W
+33/a ; The Earth Simulator Center, ,**/ B

345%6789:;<=>%$?:@2A

XYZ%

CDE2FG HIJ

8Z[W} \8]L4I2%B

KL2MNOPQR

0'S TUVW8

AoB z'$?:^<_`Z%o{ 67

A%B X  !"'#Y"<$7Z%0%12LM&[\:@2FG HGcRx:~I%$?:@''()] *^+_(*A2)^T^'`,<-'!a:9'671b2

2A%B d _ ef¡,'_ e¢(

Z%.a:bcde4 /f?'0gh(<£gh67S T¤8 671)^+¥_

2ij'12k3<l4Z%56_bcdm87'67+o ¦iUV1

nKo% 8T9 +33- ; : ,**- ; ;< ,**+ B§¨- 0'S © 1A?uvª« ,**+ e p= >?:qG@AB:Y"<r:C"12

29oB

4 ,**. m8¬~I j­U"k\UI:f'®KIo d l: ,**. ; Hidaka

e s 8 Dt:#uvwbExJ?Y"

et al., ,**/ B 6m_n'_67opq¯ghr°6

yA2VFG:[:G H(

7 ¦s '±²³´«b© ,**,ῌ,**0 t 8V:IJK4I%$?:@oB z'o{ zIm8

9'67e4L7+'+<K2 µu:vG¶

 ·-*/ῌ***0 ¸w¹y+º5»x -ῌ+y¼_ e67z
National Research Institute for Earth Science andDisaster Prevention-ῌ+ Tennodai, Tsukuba, Ibaraki -*/ῌ***0, Japan.
Corresponding author : Yasuhiro Ishimine
e-mail : ishimine@bosai.go.jp

N O » ¼

222

   ,**/ ; ,**/ ;B 

3  

cu&i(# ¡( J(M[r ,**/ ! "# $%&'(#)* +,"( t34&_-../ *+ ,0" 1

,2 3 145

1#(
{ _lnJo?Y 

x",¢&_/

6,789: ;<=>2 ? @&A 

$%$3s1ABCB&I _£"tM

D E) ( F 

 S ¤y &/-D / t S

B 5>4C ,**/ ; G ,**. p. ,++ HI 1

!"#$

9: ;<=>J% K

T S

 {&I yjp3-u(  UM[L2 J(MNOP&&-#(J) 5 C QY $%$'()-#( *+, ,**. "H"   ¦J}#' s&L 
I-&.(H/ /

(R0ST1& &I  23

45&6LUM&78VW6 9X"#(Y







&¥ §&M$%$ nJo?¨([rJ}#(,IW UM[r`")© J

J:Z[/  ;\]&M&I 

J"# t| * + ,$%$<= ,>U?Y^ JJ

(#(78R0 i,ª323 J)& Z@R00&_ AB`YCBD"#(D 4 #? ª ¡«  s/T6?Ic({{¢J(78 UM&EaFG  IbHc d 

R0_^eIJ"#(Y&I K KLfLM"#( NO ,**/ ; *gh ,**+ I i,PjQ^-#((RS(H/ IT1U9V(W _>klm

nJo?I XpYZ5qlmL([r\i£¢&.(#) Lcu¤¬

c­ %# &_

¥6¤¡«"  78

$% [ªv ,I * + ,



&

¤D ®¦"J(M§~ d R0  sI t >klm ]^_ 7

&I¬¯"( $% SI ¨°R0©

`(a&'upZvbH`"w.c±*-(ª²«¬SEQx³­-sVW6

H&"#L "H" dexH.f J6J/

 ,I  $%I´J  

^HIQy(J(M [/t W &z{]jQIH.<= t|23g-mC 6h}#i j
pmC 6\k 78MS)

~ I<6m

C 6<6=qmJ(M23B#l¯°YD /±° ª® &Iy²VW6IY $%$&J}#P&¤&}#(JµH/ª²{w 78^³&-¥6R0

m ]/  << T1&I n7¡«" * + ,l  o9¶  t · - ² &'(# pqmC 67rk >



d _´

Q  ?Y_ "#( mW&aH}#Ws"

"}#(]jQ ª c JJ)& t ]<<Y7k ?-&t J qk 

jQ&_ 7 uT1" t u vw(x&yL  {  It )

$%¡«  ·"$%!T&-zkW&t B fLFG"# µ· $% Ea 

{&U}#y|}~- , ²¡« R0Ii,) H

 + 4Q9   #({ 

²  

¶h}#(#$<=--"# % [(J(M$I YZ - ²&\o·"¸( { l$ &iY¸)R0E

-#( "H" 



0 

/B W¹Q+=ql$ ¹º&º( s ?c-JI`( ER0&»}#(J /HB'¼"#'YY $%$I78R0&Y &Uµ¶·¸z¹º6»¼45K

cd e cf

223

 + , ¨"#$ ©ª/^ 1 "#6!0« Z-<¬­®?\ (a) 1¯% !U5$ w:4°0« _G6K! (b) 1¯!U52$ <3±0«u4 V²j0 <QL@A³I!
 ´_G6:
Fig. +. Examples of two-dimensional calculation grids. The black polygon in the lower right corner is an obstacle
at which calculations are not required. (a) An example of rectangular grids used in ﬁnite di#erence method.
(b) An example of unstructured grids used in ﬁnite element method.

 D w|, 
,ῌ+|

   !}

123



cd e cf1

DIA ,  /0G*9_G6KL |1 gh GiT5

"#$%&' ()*+ ,ῌ- ,-."#78

O!PL }

gh Gi~GID^]N: 

45!6

1 "#FG g"#h GiT5!"9:1 ;<= F4 C"#V ">?0*"#@AB C #B Z +\ J01 FG! 1 DE FG #J*L1C5EJ]NG*

=H6B *IJ KLMN C=C]N?0*H 

6O!P!QRHS:4A5

TU! CV =H=> W* =>?

"#



B Z ,\
"#



1 "#G|

0*"# /0 U5XY Z[\ J =>] F4 $[T  + (a) 1 IU

D^B _` abMN c + , -  IU + , - G%d e cf1 g=>"#h GiT5_GJB&A C' Z'D1'GiT5\ =>"#1 _j0"# /0klmn(=> |

lopGq[?G^) _*1  MA

rs!tuvcd e cf 
1 w=>!"# x^6B

_ tyw

z{6tLG* f (+, +), f (+, ,), f (+, -) 

+ ,¡*!G:¢5_G6K! -<"#
1' V£.46B * ¤¥<"#1 <(¦§"#J224º  » ¼      

!" #"$% &'() *+ ,ῌ- ,-.
/0 ,ῌ0 ,1234  56789:
4;<"+ ,ῌ1 ,=>)?@AB6
C D7EFGHIJKLMNO)+PQ&'

R ("JSTUV7SWX

Y5678C`ab9Z[ \]J ^;_;c7de9f) ^J ^;_; 9&g) PQ) h9i;j9 dk8PQC lR4m+nop Kq/0rs;tuvw"
R(";wPQ9x9; ,ῌ2 ,yzSTUV7SWX/0 ,ῌ+* ,{34 j"PQ+ |8}7~Cz+zPQ9+m ^(J ,ῌ++ ,9 SPH  =>J+,ῌ+, , ῌz 8EX5c6C  , 

56789)PQ  +,ῌ+- ,6X , 5678HI (I"v" P" Jm 09" "(HI /;"  ,ῌ+. ,C PQJ2PQ Y(9 9 =>) pp    STUV7SWX¡¢ £¤;/0+¥ , w
R (JN¥ (a) K¦z 9j]J§¨;y j"¦z R 9¢©"ª«¬ ¢JPQ) {3 ­®¯ c6° + (b) z9jy  SPH  0; Smoothed Particle R (JNO(a) 9±¦z  ²³? aGIJ+ (c) Smoothed Particle NO;´ (b) µ¶´· ±J 
Smoothed Particle 9¸)^;_; Ky"m ("z¹z NO)
Fig. ,. Schematic illustrations of a substance represented by a set of particles. (a) A gravity current
consisting of numerous rigid particles. (b) A
gravity current consisting of a continuous ﬂuid,
which is described by smoothed particles used in
SPH method. (c) Fluid concentration on thedashed line in (b), which is described by thesuperposition of Gaussian distributions to havecontinuous values.

|}º»¼§iDE645,ῌ, ῌῐ῎῏

 !"#$%&' ()!
*

7

225

! +,!! 45

error) /UBE #HV3 WXV3 

YF / SE7i/  E 1W
&V" , @  1Z5"
"# [V \AnGgE* (,) *./  0"# ++
123



E "#7i # (roundo#   


6

6

#$%X2!
/ #45

6b]1

fgEh   9 K0N 

89:;<<6=>?@/23 + "AB

6d! I 45^_c K!eF

df
Cg
dt

(+)

6
`a/.DE3 v/blEN Ic l`m 

#$%&DE  f, g  FG

7i?@ d dFJ` (trun-'H (+) () IEB

cation error)  dFJ` ! I$% *J?*+45

0T,X2!/¡d7i fgEh 

6 KLM6>45

6N #$%/,-.() O

  fgEh /I  0 ,-.,- $ K!eF 4 9eI$N ¤f!

/PQ!  KRS0T,/U

/%H ¥gI "AB (+) Y3BEN 0V3 #$%1W,.X2V3
 "AB (+) Y3@ 3
fKtoZ[tN\fKtoN
df ῍ῌ
dt ῍tCto[t(,)

¢£k,fKtoZ[tῌ,N\fKto\[tῌ,Ndf ῍ῌdt ῍tCto[t(-)/X2!$ (,) `X2GHm` ¢£¦h§iI (-) ¨ ©://X2! (,) ] to ^_+#X2

UBE

&V3^` [t 1W4ID5@++a«¬;:6/UBEDGGHU(+) (,) b23!/ 6c d !eF* / fgEh
7i jk

&*V"oªmbeE3  >/ X2jIn !*­ /DEGH23®U GHU/!E*89 237.:DE";<B ?*>¯¨° K±@+SEjk 4

=>V3 ?@l2"m;<23

5

Vl 

<! N O~` +nmonV3AB!nC#D"23 4I

6URSkl12"?,m^.

 EGTo+pqV@@ WGE"45

pE/7.:!F? d

6Rrjh¢£:! nse"236c¤fDE3I

b$%q0  GH*&*" 0"# tu²)! v6I3  / !eF (+) r3I wJ!

J sL> %H

,ῌ- ΐ῍῏ῑῒ

X2K 3  *Ht!Lu%m

6 F j&8+/V3v MwX2xy4Imz{

1W KFinite Di#erence Method l"xV3

 V"23 |}N|O~*

FDMN GE (/UBE/! Mw fgEh PQ

 1W y +(a) ³zb2+$R  VnV E+89H3 ´+U,-+{!.! µ!SE` ;:;I  0|}V"+#/~6 (,) (-) "# T@ 3 EUVV 

X2´+#&*! KX2RS

7iF ,  d/V3 45

6

,N , t¶­ - t¶´+&8+! 1W _&DE3 /G(·¸c¹V"+a³zUL 6!

¯ ° » ¼

226     

tJ (g* ' tJ 9 ;=  ! "#  $"u,0X0m30

() *  + ,-" vw0x .G3Uil 

%&'

yXGN &( 1 U2}z , ./,01 2'3'
45675819:;"<=/3' > ,?-'0 9 @? AB C

D3    E-F !GHI"#$ %J+ !&+3"#K'1,0 9

'-F 
}({9B -=/3* |;}~=/3' $9''["Z'-F  @?-19
L*4 f33' 

L*'M/'* X/1+xU'BN( OP)E"9*Q +R-9 B /3' l

,9-.  -.ST()G3 U
VW/(,0XYZ" [\]^_` L*%J
M'1@?M/ a-F bcd2,
2-Oe=/3' E

33,?

-0&+a1 "<=/3'B Pv"-' - BN(
3YxU'-FD¡"EDK fg'aG  3=P?/h i*4'

,D-"-' 2}¢gM*-'jk5M/G9BM'G'l67 09£ (+333) (g*' /89,:;=m3' <n=N(S,/h)'3

9 Connor and Brebbia (+312) Wy (+332) x&,o*> -f3pN:?3 @'A+¤,¥l"9

PGgB/-jk f3LlgM  a¡G3M/3' L- a )

ilpN:?9 2CqDGrh/3' E

ES-PvG392C'}N_~ (+33/d) :,EFGHI+sk"#¦y (+310) Y Thompson et al. (+33.) 1  aJK ES-.tLM) NXO=/,ῌ/ ῑῌ῏῍ῐ

3'

5\§cBN( B 9 A

BN(
'

uPv9-2  QU

-, GG" Rw3'

Press et al. (+33.) xSU' TUV*

9WXyzY (+322) Z[  von Neumann Grh/,'-2CqD{\ -=/ TVD

V9]z (+33.) (g*C G"rh/ A C 9 E/(¡: :¨r©v · grad!rª«rdivv¨t(.),¢ N(S3 aa r 9!£ v 9¤¥3' ¦ a' BN( ,'-9 a|^D

ilN(S,lG :+ 9(D -/9¬B HI GG" 2C'}N_~2CpN if3:­aG  (+33/b, c) 1"`V*=/3'

upN9¬g f3" H:+jk,,ῌ. ῑῌῒ῎ῐ"-M®¯x  §Ph £°c±²C

AB C Finite Element Method L-9

FEM! ,V* a,

G3 

f3D3''2 '  ¨3LlaG  ailJK,³©-F

BN( GbZ<'M/3' B EOe=/-F9 VW,cn+L-9 FVM!  !

( AB~ C Finite Volume Method, 9 +d

B~ 9 ´HIµ¶² + - 9defe ((gyO! ,f3 ,aG p3,laG  h +b!

G3l +deij=, ()klm &P3noaG p+.,'0 !HIG,?-'01

  qe p noaTrD
sW WggG'l1"  "N,ª« ·1,¬*¸¹~ Vo    f sW"­,¨ ῏
ῑ fv · dS
fdVª«ῒῌ῎¨t ῐ῍῎

(/)

G¡3N(S - dV 9~® dS 9º

¼¸2¹S ºPQ G»OLEJKLMEJNO
 Vo  

 So

 

 (/)

#$

(/)





 Vo   
f " (/)

 !(.)



227

 TU" 7  hG

P< F!<QI "l  {UE);/ 7m,
A5@"  OLEJKLMEJNO

%!&'(, 3XIZ" ?")*+ !!,-./l f=: VPQ A5g  Xql

0 "1# $%" )2 &" `F!c fEO = A5g )" 3   456'(7)

F

8 " 3

95 *+,F!c= G*;

-.:3";/01< =>? )2

=q!+A5" l' 3

rse fGravitational Many-body problems ; N rs*+@3 4A5 BCDEFG6,(g xmQ #Grs!d 
OLEl)"*+" 3+78H!I> JKLMEJNO I(9: ;<(G

PQ

95 =R' > =R>?S
JKLMEJNO( BC@TA!

(/)

D"UE F VWG ! =R' >+X =R>@H! ?S
G< =R> Y(IZ!

9Q+

?S[\ =R>]^J_K!(!
  LM (+33.) 

ment Method G¢<£%¤ f¥ +332g FJKLMEJNO Q
;GJKLMEJNO  PzG;¦§>F
aO,hijklbc!)Pz!
"  G)JNO;/ )N`)B " 3 )
bcd>e fBoundary Ele-aOP5 Q>(^m F! (Ebisuzaki

et al., +33+)  b hO O¡ He

! c)¨§!

 ¡c,/¡O0/¢^ mvnJKLME,ῌ0 
(/)

b;G

BEMg 

hijkl 

!

Y(£U

#"

f¤6

+33. ; Hut and Makino, +333g,ῌ3  

?lq¦,¥h A5(¦,GrRS   TU! N`cd VW!XYs > OLEJKLMEJNO{,&') ^m= 1)noZ

Q[5\]) ^!I> pq_r3`a@3F bcPQ
_

Q@3

f

8J de%0g]?S3=)

b 5#JKLMEJNOe (Molecular Dynamics Simulation) xmQ
©§ BlWªE (MD) xmQ 3(G «,Q¬ F^ ­,®¯h f^m Amber  Gaus-

Brebbia and Dominguez (+33-) hisj (,***) Fsianng ¨! °±²±E³ ´²±E ©µ bcPQ,ῌ1 k )tl)uJKLMEJNOFmvn)  b/w>e xmQ #@>c/w>  cdoyD"z+*3(ªP0/)¨  +*** [ ¶c)!  JKLMEJNO «· ¬!(Narumi et al. ,**0)5#JKLMEJNO  )­hP<

p{|7;}~@UE" Q>

" 5 ¶t>¸²OJ§®|%p{|7!,EjBc 3G< 3

UE" G ¦,(! ¶¹ Bl[ !) +, ¯3 q!

^c rst ,cduY7 R+Q FvY ^w|7

UE"Qmxyz< P{@Z+Q(,**.)|}!<H~PQ°"± 0 ¯:
3=UE º #,ao]²" Q>! b³8¶+, 5#)e f ³8¶+
)g  > }´¶VW*0»5  F

,ῌ2

Q

*+l

 *4! 9

Hoover (+332) · (,***) FF!c " +@  (°";}~ Lennard-Jones ¸²OJ5#JKLMEJNO&µ¶£ ¤ » ¼

228,ῌ+* 

SPH fg-$*S (             !"#$%&'(   !"#w  fg

 !"# h;8'(i=m>jx+kyz{lk,% |]}~+, (M SPH   Smoothed Particle

V+ky m no,a9  [)*+,  -. fg-dp[9)*Y SPH qr-+/,  0&120)*st (+33+) 672'( uv1 (+33,) 3

 ! 4Distinct Element Method 50 DEM6  "7 ! (Discrete Element Method : DEM)

6

,ῌ+, 

89   ! (Particle Element Method : PEM),:;,3 ! )*+<#=>?@AB$ 8C%DE&'8' F#=>?@A(M+(


,FwJ ,)GH* , J xyz8 >! 4   [Ht0+, K+ ,-

5t09~

!"#

.-

 !"# /#=>?@A KL 
0+1/

MNOH*)*+ F0

aB.8'(E

5t0{6 Ht050+  8)GH*IJ)*+


- 

(



 |xDY k

 F0& })J ,JYX+m~ [ -

 KZ V+,(} Z@  F -& 3 !)*2 34 , 56780

+E

wJ ]  ,)P8 ()*8' 3!)*80

3 ! QR 9S+, :;T
UVW 4Hard Particle Model 50 Hard Sphere
Model6 , QR :0,+<= UVW 4Soft

 \A

. wJ J,oMt'(E J ]  (,Particle Model 50 Soft Sphere Model6  , >?

M $H*IJ)*8' T+,(Z@UVW + 0 +  8MXY (,Z@Y[  \A BC DY(])*+E^_ 1+ <= UVW < F1  ,8'([ ])*+E^_, ( + _`GC a

.,

4@A#6 2| MJ ] $*2 A

!#n@A#,:; )*
DY9 +,



.

 +0&d   8M8 ¡J JJJIJ

9 HbBC I2(J)*+0&12

9

0UVW  <= UVW 8 cKY (E ( [ )GH*+de%fg, Lh- !")*+A! £¤!n@A#,# *Y 4M +3316 3 !N

OPQ i (+332),ῌ++:; OP ( 3 !,|' 
i (+332) 67

SPH  BZg¥+¦§,8' J,   8'(qJ -i¨  !"# J )*$jR
&'( FNS

SPH  4Smoothed

Particle Hydrodynamics 6   SPH  k=l TLUC VD

.[t'J J ¢8 de4mn> V*(D  ,**,  ,+ © - ª  ,ῌ+- 
«¬W­®#  ¯W°!£®£#,:;

bUVWMX80J )*  ¯W°!

KW6  Smoothed Particle ,:o F#=X£®£#

  !"#,YZ+)*+ + _².Y  } F8' F ` pq ro80  092o 5,². ³´} µ~T0|')*¶[\)/+ µ~+; ¢·s]2'(,%+b6 _F ,Pt' Smoothed Particle

 4^ ,
8 u-M±&20)*«`IJ

- ¸ ¹F#=X Hb

G(, , Y k=` 8uJ¡ ()*c9SY  ¯W°!£®£#abc , t0 VD Mdve,¢ 

8'-2

¯W°!£®£#}+º(' ®  J

\HU¹º®+!@<»tO0¼MNOP0MQ
 

  "! 
 #$ %&'(), / 01   2 ) 3 +789:  ); <78! "# =>?( @<$%<) A8  @&

tional Physics ,**+ v Vol. +03, Issue , 3H.MNO

P0MQ$4 7 <!

*+,!-  & !.
 , 4 56,229



--ῌ+ 

wx \Hy\-OI=F:!( MNOP0MQPQ \Hy\}AAv  Nz{M|`} 3/4 N.~  N_G3U

>B '(

v=F$  @<J<-O^J)*+ ,8!C -@<$. /0r

1 D2  & 23E4

B9 <v== >aB<!Jd

5 =FG678=<> 9H:< , I;
<J<K=L%<(!$> B

=F:bx  hijF)

Y*<:+8 <OST=<=I 

!(B? MNOP0.FMNOP0MQ2 "?R:  H

MQ<stui3.) "#+!@=  {:(NU*v[FXSABTEC (+333)  H.UVD!WE (,**+)

FX+!= /N-ῌ,  !"#$

. /4+!^J78 N`},ῌ+. 

>

YZ  K=)[G FX \HI 1P0sisih<> < /3G6E45 <(. /]}{M| p <

avN`}; <L `}^J_ KLM`aB<<J<=bL N

M¡¢ :( `}9£

=!<> K=78=OS99c& |?={ :(=L M¡& M|

<PI@=:( \Hde  Q8C R

T¤ (= M|{ >B LST fg,8hijO0U%G6_ kl

<% 2 h¥laB<L < VWmXnopVY#GH1qrh

2 /i } U¦`}i<> K=L#Z[<I@=

a% += & K=) MNOP0MQ Z[<stui<v= & L <v M|{

L#  }& §2!
¨

K=bL\] <J<^  _`a%w
 #=@=:  K

/ <78=   3,ῌ
+- `4 #= Hersum et al. (,**/) _ Niimura (,***)=bx M1 <bL =^  <>7©v= ª1q0«#=<;yc!Jdz{kῌhs0ih!Jdy|

J<bL <K=m~ 7 FMNOP0MQ @Fe5(!= aB

2 }! ¡¬­  3,ῌ- `4 #= a%

<Q  23G}G6_ bx fm~ <h®0 I ¢ 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 _P rusm~ °± M0)² =B@³¥3

(Sussman et al., +33.) <>56,@=´¦µ¶)+!==D)  CSF  3Continuum-ῌ- %&'()*Surface Force  ; Brackbill et al., +33,4 aFl(!

 avU¦:( /=¨ <(~©¡

/ § 

:  @F^ \H

K= !mnA ;o·q=v ~_&78(!= N(+33/e)  pdq<r¸F`} /a%ª£i+FsWt (,**-) [P{O0= 

ul% =^  Journal of Computa-

/U¦`}i«%B+ ¬­:(

C ¹ » ¼

230

 

" #

8s -9 Mti]

  l'v1)  \? f  GABCDEAFG 8,ῌ+. -9  u.//a  

!" #$% v  wxo_4'/jz 23\?t 4zLH! 23yM& ' ()* 1)+,-.! /" #)0$ %_;<}&E 0~P)Q234')*( )5/*6zh/3Z 23&1

7+, 8,ῌ- -9 ).

Kuritani (,**.) :;</1

Eo {m|:oZ~P2 4'* 4m%  

-ῌ/

0 +=>1/2?& 2@ +34&ABCDEAFG 8,ῌ3 -9 ).
*(H! 

8I5'6J +331 :9 K

ab o_`o0 /k:oY 8, BEOP#9 Eo_+
 E L78)MN / #GOPQ &9/ qT +

:R ;<)=  STOUVWTXYOZ1/ Hf)>Z[\? 8,ῌ3 -9 2@A ;<:
H! J-i 1oJ`^  o_`1(Iitaka et al. ,**.)

 3/qTo_` *67+, 8,ῌ- -9 -ῌ.  ABCDEAFG0)5 # B]^CD`ABCDEAFG m< 2 M , E_  FGH` <)Ia+%

JK LFbM/0c FV +** V|9 )`

Z@ jz \? 8L

234'*( *6&9, 8,ῌ. - ; dN'Q)4 ` Y B¡¢T

OP ,**/9 ef&9, 8,ῌ0 - ; Dahm, ,*** ; Mériaux*)

and Lister, ,**,9 Q. 

L  ` <R

3Z@ +:wAE{/)}7Sg Th*( *6&9,

 `B] b|(Ryan, +322 ; Saunders, ,**/) ef&9, (Cayol and) jz

Cornet, +331 ; Gudmundsson and Brenner, ,**/) U.{Y¥1/)< / 1¡£¤¢) 5jkP\?

£¤{Y¥ ) i)5 
# i.! /2V

8s .9 8o_q

T/Mivi19 =>o_Mt¥¦ # L!WX9:Y% ¦§:) §¨P23/ ¨jk$a I. l4m Z[\i© !" o_©@ªª«P¬E2Ml)#n(Carrolliª«¬)­ mg ¥4M®­o_`op

JKbh /323Z®¥V¯T) /i]/(^1and Holloway, +33. ; Tait et al., +323) ab   (^ qT+" #r)s /0c  q

T +. tc +d u . +qT
+e% HfTgh

iv Y^L Y^wExy /3jz pT{
YP`o

. i]kj LLl)m% / )n|Eo 4' 8}~
GEAFG9 g n| 

%¯w4 /)°s°± ;</ Wohletz et al. (+32.) 2± P o_3/qT +m²  |²)Q m³¤ ³I.) 5jk

!" Z3´1X¡¥

GP 8,ῌ+, -9 1µ ;<0 bT P)bS
8Clarke et al., ,**, ;Neri and Dobran, +33. ; Valentine and Wohletz, +323 qT +//oJ`^ ab :9  0 `¥4´+b`o1¶`µ  `µ¶_/·ub]4'@ Kinjo et al. (+333) =p ' q

4'­Mi2a} -i 1oo/(,**/) : Lennard-Jones SGAP)r +3

G¸

4&ABCDEAFG 8,ῌ3 -9 ))5$a 



M

+¹{º·¸/~`º»InWfg6G)¼B¢>@Q<=>?@<AB 

231 Oberhuber

et al. (+332)   Dartevelle et al. (,**.) 
"
+

#$

,-.

 !

%&'( (,**0) )

*/01  23456 78 9,ῌ. :;<=>?@<AB

(% (+33.) C)D/E61
FG C23HIJ %KL30MN O
P56QRS T U .VW.XYZ@[\ ]^ _\`K56Hab
c d6C

!

eRBfg3061 h"# i$

Uj% k3T&l)mn'( o)3 p
 -1 'JKy<=>?@<AB C6L4³
OP 9´µMN¡>;1 , ³'¶·bO
P C6L4³N OP/  QR
S5T0U VlH S5¸0I¹§
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 toinstantaneous expansion was investigated numerically. A bubble with several solute molecules (red)appeared in the surrounding solvent molecules(white).

qrs)t*+ ,u56v0)w -0306/I01 xy -0zg6.

{.

3 |}D /-~I.E^ 0)v.Ms156I2zg306 (Armienti
et al., +322 ; He#ter and Stunder, +33- ; Tanaka, +33.)1

QRSOPT 

3 4-fg3065

67 56 9Hurst and Turner +333 ; 89 +331;15) '(:0T GI ;56  E6v05z G<=BQ@ (Volcanic Ash Advisory CenterVAAC) v0
}[@Ifg hI.<=>?@<AB M= >3061

 .1 H<=>?@<AB 9? @¡>;1 ¢£¤¥ +33+ AvB E6C 2 ¦ kgῌs§D OPHi$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 rateof 2.*²+*2 kg/s, which is comparable to that of the Pinatubo +33+ eruption. A vertical cross-section of themass fraction of the discharged gas-particle mixture at +.** s is depicted.

¡ » ¼ ¼

232



 

  ΐ
!" #$ ΐ%&(,**.)  ,***' ((,**,) ) Seino et al.

*  !+" #,῎-./0 #$ 1((+333)

2 3῍4#56


7#8 !"#9$:;<=

= v    B # ῌ "   R  z A (Gri$ths, ,*** ;Manga and Ventura, ,**/)$ z"!ῌ9=v

A#xy2 G '2 )#9
|B0 ^[0C: ῕ W
p# (Hon et al., +33. ; Kilburn, ,**.)$VUW2 VSῌA# ^2 H=fMqVJ2<  
Wp#$ &74Q ῌ9=vA#

#% #$-ῌ0 

,|}2,tuB8 z=va

&>? '2  2()*+῏+ @ABCD ,῏EF GHIJ" #

2<aB9^[_J" #$ YBabW,G[!" # '/

K- #$ L.B/0 E1M2 !)0 ῌ", )B^

3(4A#N567

`KA# ,  #$

2 8OP9A# Q,  #$ :;<B

xyΐ'2 Y)J @,ῌ- XF J2Y

P9A#=RB῏+ @STF IUV0

J @,ῌ/ XF  , Wp#$ z"! ,2WRB$2  #5M4

STXY>? 2 Z@ABHB, =+"#$ 2+!/Wῌ"!Cῑ/P9A#DEP9 [BF῕0+)R  %#P9<B-M,

' !G[!" \] @Minakami, +3., B^F  @ r¡¢£¤F Wp#$

H

Q2 

1W2IJW_;`KA#abcdefg+

¥ῌ)¦ῑ§O z,A#{|Lῐ" # (Mastin, ,**+)$  ῑ<B @¨v©£¤F Wp#$  =RB῏+h0

=R L%!"# ijbklMm 4QBV

῏+ 22nNOPQoWR#

2 ¡ª((+32.) Miyamoto and Sasaki (+332) Youngand Wadge (+33*) B^p#$ « 2 ¢+7

4QBRS2JGT+" B4QWp#$

z,*+ Qx£1¤¥ qUrcrsR B A# itu£5M ' @Costa and Macedonio,vMm J2 iVSWm,**/ ; ¬(w&"#=vR!" B$ z4QBSTB^

S<Bxy῏+IUV02 SPH J @,ῌ++ XF RSY{Wp#$ ΐ%& Z[((,**/) \4S]>A# Cῑ Z@A{|OP^[_8& YB`ab!"# }c+"#$VSῌ

p#$ H1W2

VSῌT§ !῔(°, ῌ"B#ab®
^[_G - )

g+"

#

@Hidaka et al., ,**/ ; ¨ /F$VSῌB T~] ῌ".#$ VSῌW2gh­¦῕ 

OG[ΐ (Crisci et al., +333)

B&ῌ".#V-ῌ1 

rcrde+"BJJTfA#+33*F$ z(Favalli et al. ,**/) ) ®¯jrjJ @,ῌ+- XF

QE

!±#

X*W©ªA#«¡ῌ eῌ2 ²¬A#hD­ #$ 8 RS
-M, ῒ¤E'$ n ®³B

{|=R iῌ<BP92jk+"#$ 8

=RBRS´O+:#µ¶ELῐ;<= lG [B+"D

YJ @,ῌ/ XF '²¬

Wp#$   #m2 VSῌnYBo#p

n~Wp#$ zE2 ¯°)±B^ *· ^2 -h<W+%WqVW

64#&ῌ" Wp#$ 8 z"

R#rs B$

!VJ 8 ῕ #²¸ p# (Denlinger

VSῌtuWp#H=6

and Iverson, ,**+ ; Takahashi, ,**+)$ Beven(,**+)³

2 ῔) vwxy VSgh=Rz,A(#z Wp#$ z8 VSj){U|}B^-ῌ2  

VSῌn~<BBA#$ & g«¡ῌA#xyW2 XW¸¹¥£5hz,yVSῌῌ9nh=Rz, vvVS VS TUVS Q8(+323) B^²´µ¶ ·LB#$

MY)J @,ῌ- XF W,ΐ'
@Laigle and Coussot, +331 ; º¹(¬,*** ; Z»(º

R9® »³§"C¬^¼[\YZ[2\Y]^233

AWXoIpRS?&TUYZ[
2\Y]^N > VVO +31/ ; Nomanbhoy and
Satake, +33/ ; Tinti et al., +333 qr0 R9:R st u;=vw&YZ[2\Y]^Ml VxW ,**+ I 9X AyTUY="zN  VZ{ ,**. >5-ῌ3 ῌ῍῎R| AWXBC }~VX<.
;u[07'05 !R9AB
<.I\ AB+,D X]^ M_R|`ab;R9HI~ 
 / A YZ[2\Y]^ VOµc 9 -. R¶= ,** m-ῌs 0A¡&¢i N
0 <£ ·-I¸¤ ¤¥¥8¹¦2º .®D
&Cn£7
Fig. /. An example of lava ﬂow simulations (Courtesyof E. Fujita). The lava is assumed to ﬂow from avent on the southeastern ﬂank of Mt. Fuji with arate of ,** m-/s. The lava spreads towards Gotenba
Station under the inﬂuence of topographic heterogeneity.

Cce=&  \]^ ='"H"05 u056>7'deQ?R| S?fr ghstN ij=`kJKm*


N R|

=

(lm*

]^

 X]^ X8Q?> !e=/\_n (granular ﬂow ; Duran ,**, ; Jaeger et;al., +330) 05  :oghp X]^  \]^  Vi # -./h q=rst0& uv (Branney +32.  



   

C-./h"     !" #$%

 2  X   \ y^8 +=&'()! &*+ ,-.

, X8/0 &1 0!23/4 05
6 4 7 

and Kokelaar, ,**,) m;

R| \ z{YZ[2\Y]^q>m;!"#8$9

 \ 7'= wx Neri /\E05 (Dobran

et al., +33. ; Giordano and Dobran, +33. ; Todesco et al., :%&'&(7');6),**,) | 3HR9}~ 8 < =>* ?@ !AB 

H¡¢&N 7(<R| \ C+,-./D&EFGH01£ 4 ¤¥¦_&= §X¨

2 I JK L3M0456NOO C©=ª   \ R

7 !P82 5 6Q?

|

Ishimine (,**/) I¬F^ n 2­HR90

R9:R; <S=I<>0?TU@9A
 VAWX >  YZ[2\Y]^J_BC`D " (Heinrich et al., ,**+ ;\=bS&¨«N:R®  MlN Córdoba (,**/) 5¯N0 BC 4U , ° z{-./0 X]^:%&

Kelfoun and Druitt, ,**/ ; Pitman et al., ,**-) NX

K05 VItoh et al., ,*** ; u±n\ +331 BC

0 abIEF0cd"44;

-./ No²0  >5 (Wadge et al.,= >N",  AWX0e=f'4+332) n9O (+33.) 0 X \ e=

gGQ?H0-./h?

l *zN-./ |

T ON AWX9i4 !B

f014  \]^ e=(7OO;e=& "IJ jK'5O Ok70!

1$D V,ῌ+* L  7'k7&Ml>m* VCampbell et al., +33/ ; NOnPQ +33* 6 \> 4Y^E//\¬\^-./
VR|³´/\ D; 8 » ¼

234

     {GA

wuwq Oqy |U#I( Malin and Sheridan, +32, ;  +33- !  ,ῌ+*  "# $"  (Mitani et al., ,**.) SPH  ,ῌ++  "  (Nagasawa and Kuwahara, +33-) %&'( .

_ `Q OPQR OS ) }~ TU3>4%Aq Ob#I-)F-ῌ+* 

>'( - GWH^a2 TU ) ) *+*,  'PQR OS 0"Iz>FG84(A^( - ./%"#) *+*0 123'

|'%Z %W-d"#I( ?01

43 0

Aj'! 523!6# 17"O

.%& /'3#v%J<

-8- 9#:$%; ! &<'=!>3 ( QAc ';

3b/e%w

"?0@!)3*+A%& B *+*4R3"#I '( ">" -F)

0,--."##:C"2%/ 9*+*D

a&%G8& 2W3 %I( #:$%; %&0' 012

OPQR OS+332 ; White etal., ,**-( ?!0 363!4>"# 5%/./%' E

67 ,**-( ">" -F G8) H!C"
I9:I 0;%J<K=>L%J<M?
N@A%&  OPQR OS TU)) B3YZI#CDG8 E
\]GWH^0 _[%FJ<ATU`Q  )a\]3VF%I( bc
Idef¡X&)U'% ¢3'W

F%£00¤¥'( TU3_`Q OPQR OS  3¦"#I23) a2 §$¨"#I>%]c%F%I(
Gm u> §) _ `Q OPQR OS
3GW ©TU W0'3%II/'(  fd Mo'  9; 3'VWAXI%I(
V}~

3gI#) H !JhK!LGiªOPQR OS o« 0¬#%I
I/

0 - Gm'3d"#I( TU

3gI#) Y'% TU37b#­R%& z[i!

f!?f ®Hf3

3YZ2jMklm n NO%&3o"# P[

YZ2 QRp

 W%ITUA#12"%]c%F%I(

PQR

ST%  G"#_ `Q OOS F3)

E

Q¯

V

AU0V2Q#I (Epstein- G x3A OPQR OS TU3P°

).%>6 qr

±2450%II/m)"cF2>²%I(

and Axtell, +333)(s _ `Q %/WI#XJ'3

 OPQR OS )!b G0

G85YAZ ! t!'uvwxy z[{I q³F#I( _ `Q K=) 'F|%& }\  '~3]A^ '´ e%!Z 3µ6'%HF"#I

3_`AZ %&IOPQR OS aI(

( a./%Ez

¡¢£7!!b¤¥) #W   co"$]0 & ./%¶0& ; L%/A

H

e%Oqy (GIS : >3I#¦:)%§ROPQR OS

Geographic Information System) "TU ¤¨\©IªX a {|3YZI e%

!bo"
#_

`Q

dA

aI( bc bE P fg&h!
"3.k'ij(lm)[AOPQR

OS %&0AF#I  efnTU %«3!b#Fb ·¬"#I#0©¸)%I( - ./%·¬OPQR OS!befK=TUo ,**0( f  @,3g
]TU OPQR OS*pb+I0I2>'( bc Aspinall et al. (,**0) )Gm k¶)­"2>4I(
¹z"./3  %/AG8
a2)®'%¯°0º­ G8a  0#±
'( a   ) :8f!M»²f%

qrR! ,(-%& z[ I&#  st;~  G" uv%R_(  ¶#4&%OPQR OS K)³´"#I%Ia2¯µ%m0/`Aw"#I( Guidazzoli et al. (,**0)=)·x3A40aI)Ib aF){|xyf'%TUN|%W¸ ¡X&) a VV)G  # yzs *Ez3 84b83¹4%I(   ¯q'~3º¼"J

OPQR OS

4abe »£¼¼12'»#%I!"#$%!&'
 





235



t 8x`  EV54!"#$%

   

!&'yzc{.2T 4ab!"#$%!&'()*+ ,| ?.+ .` V *<-.!"#$%!&'/012

J*

3  4*5 67 8()
 + 4 9: 6;!"#$%!&'*

῏

<

^3ab} ~ ab!o ῎

44* =*>212

?.+ !"#$%!&'   4"#$%!&'PQ

!

6s/ab}^!

 (<E E

4!"#$% 4&@A*BC?.

 ^3ab} ~ *siab

>  3 DE2FGH%

4  "}*ss   k

I  =*'()?.*<!"#$%!&' >2JC*+K >L%I,M 
DE2?.-.

* 8/NOm%|%I!y\ ¡p t#  $ 32¢2%.8 tb£¤ (<E

6s/ab} ¥¦  ^ 3§R 8PQR >0*< ;S1¨5 (<E H*2+ 3 T8PQ 3;> 45M*skab} ©>ªh*s 6ab6. + 789<: ;

}  ;> «l;7 ¬ ­;®*)2U> ? T 4 !"#$%!&'

?.*<E ?2> $;*;;2  V <W T=. X

¯ E b
4YZI[\> *<!"#$%!&'/M  ;5 &].?@NO
A 5 BC^_  !"#$%!&'/DE ; `  !"#$%!&'

*/¡3
mn±

6s/ab}°4&..4 6,abijkl²³%´ °4µ¢fª46¶& !"#$%!&'/!|µ±

6u.  4

!"#$%!&' E.+ *{£¤¥¦ }§¨~/F7 GabHRcId R TJK5LU4abMNe Of
PQ*< ; Tg  
E hQXT !"#$%!&'RSTU abH 4, ijklmnabVopWq5 `  44!"
X rstuvsU abHwt4x
y zY!"#$%!&'Z+ {An et al.,,**- ; Tanaka and Yamamoto, ,**, ; [\|T ,**0 ; ]^|*} ,**/~ ? TF7abH] > G*+ abH_54!"#$%!&'K5Luv`a ?.
E2
b*=TJ

4!"#$%!&'  *s$ cdeVf ghi* jsH*+Kt8
>NU ['Fmn ab*<k*<;>* labmQ: +*8  no!p*qr:2U 6s5F'*t5!"#$%!&'/*<uv+ wtῌ ῑ ῐ ῍Aharonov, E., Spiegelman, M. and Kelemen, P. (+331)
Three-dimensional ﬂow and reaction in porous media :implications for the Earth’s mantle and sedimentarybasins. J. Geophys. Res., +*,B1, +.2,+ῌ+.2--.
©^ ' (+31/) +13, ª«(·¬`­O/ k , ,2 ..3ῌ.0*.
An, J., Ueda, H., Matsuda, K., Hasome, H. and Iwata, M.
(,**-) Simulated impacts of SO, emissions from the
Miyake volcano on concentration and deposition of
sulfur oxides in September and October of ,***. Atmospheric Environment, -1, -*-3ῌ-*.0.
¸)®0|¯ *° (,**-) *±¹4²+ *±³!"´º.»%m+,7  µm +/ ª$¶spab!·p¤ ,-.ῌ,-/.
¸¹6 (+33.)+Ns *s:ºp ,.2p.
Armienti, P., Macedonio, G. and Pareschi, M.T. (+322) A
numerical model for simulation of tephra transport anddeposition : 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. andHincks, T. (,**0) Using hidden multi-state Markov
models with multi-parameter volcanic data to provide236º »  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. GeologicalSociety 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 inmagmas. 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. andDruitt, T. H. (,**,) Computational modelling of thetransient dynamics of the August +331 Vulcanian explosions at Soufrie◊re Hills Volcano, Montserrat : inﬂuenceof initial conduit conditions on near-vent pyroclastic
dispersal. In The eruption of Soufrie◊re Hills Volcano,Montserrat, from +33/ to +333 (Druitt, T.H. andKokelaar, 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 simulationof 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. andSpataro, 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 geophysicalgranular 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. (,**,) 0123456707189
:;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) CDE5FGH7
IJK-LM.N OPQROS. 5 TU
V WXY8 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 (,**.) hijOPQROS.7klmnopqr abs4tuv!wxyz{qr|}~ +-  O.Ln 02ῌ1+.
0D4E (+332) 0OPQROS. 
A ,*2p.
῍8 % i  (,**,) hi¡¢/£¤J¥,¦§¨©no7 eªk4E« -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. D., Neri, A., Bisson,
M., Ongaro, T. E., Gori, R., Pareschi, M. T., Calori, L.,
Imboden, S., Cavazzoni, C., Erbacci, G. and Menconi,G. (,**0) An interactive virtual environment to communicate vesuvius eruptions numerical simulations andPompeii history. In ACM SIGGRAPH ,**0 Educators
Program (ACM special interest group on computer
graphics and interactive techniques eds), SIGGRAPH’*0, ACM Press, New York.
¬­® (+331) ¯°OPQROS.5¨±²³´¯°µ¶·5 ¸¹\] ,-2p.
He#ter, J.L. and Stunder, B. J.B. (+33-) Volcanic ash forecast transport and dispersion (VAFTAD) model. Weather and Forecasting, 2, /--ῌ/.+.
Heinrich, Ph., Boudon, G., Komorowski, J.C., Sparks, R.S.
J., Herd, R. and Voight, B. (,**+) Numerical simulationof the December +331 debris avalanche in Montserrat,
Lesser Antilles. Geophys. Res. Lett., ,2, ,/,3ῌ,/-,.
Hersum, T., Hilpert, M. and Marsh, B. (,**/) Permeability and melt ﬂow in simulated and natural partiallymolten basaltic magmas. Earth Planet. Sci. Lett., ,-1, 132ῌ2+..

%623Qµ¶·¸l¹º!mn»O¼(*&'()&NO
Hidaka, M., Goto, A., Umino, S. and Fujita, E. (,**/)VTFS project : Development of the lava ﬂow simulation
code LavaSIM with a model for three-dimensional convection, spreading, and solidiﬁcation. Geochem. Geophys.
Geosyst., 0, Q*1**2.
(+323)   ,/,p.

Hirt, C.W. and Nichols, B.D. (+32+) Volume of ﬂuid
(VOF) method for the dynamics of free boundaries. J.
Comput. Phys., -3, ,*+ῌ,,/.
Hon, K., Kauahikaua, J., Denlinger, R. and Mackay, K.
(+33.) Emplacement and inﬂation of pahoehoe sheet
ﬂows : observations and measurements of active lava
ﬂows on Kilauea Volcano, Hawaii. Geol. Soc. Amer.
Bull., +*0, -/+ῌ-1*.
Hoover, W.G. (+332)    +10p.
Hurst, A.W. and Turner, R. (+333) Performance of the
program ASHFALL for forecasting ashfall during the+33/ and +330 eruptions of Ruapehu volcano. New Zealand J. Geol. Geophys., .,, 0+/ῌ0,,.
Hut, P. and Makino, J. (+333) Astrophysics on the
GRAPE family of special-purpose computers. Science,,2-, /*+ῌ/*/.
  (+332)   !" #02 2*,ῌ2*1.
$ (,**/) %&'()* : +, !-./"0!" #$#1#23%&'(423 5%6)*789':;<= +> +0 ,-23>?@A..3ῌ./..
Iitaka, T., Hirose, K., Kawamura, K. and Murakami, M.
(,**.) The elasticity of the MgSiO- post-perovskite
phase in the Earth’s lowermost mantle. Nature, .-*, ..,ῌ../.
BC.DEFGHIJ (+32.) K/LM0L1
&'()&NO +32- ,P230L1Q45%6 ,3 S,.,-S,/,.
B67R6 S (+33.) %T189$UV/W&'()&NO :;XYZ< -0 ,,ῌ,1.
Ishimine, Y. (,**/) Numerical study of pyroclastic surges.
J. Volcanol. Geotherm. Res., +-3, --ῌ/1.
B=[\ (,**/) ] %T1 0L1&'()&N
O^_W`> #$#1#23%&'(423
5%6)*789':;<= +> +0 ,-23>?
@A .//ῌ./1.
Bab (,**.) <c;de?f!
gh @iAj ,.,p.
Itoh, H., Takahama, J., Takahashi, M. and Miyamoto, K.
(,***) Hazard estimation of the possible pyroclastic ﬂow
disasters using numerical simulation related to the +33.
activity at Merapi Volcano. J. Volcanol. Geotherm. Res.,+**, /*-ῌ/+0.
kBlCDmIR (,**/) 8Enf!opoqFG
Hn_Er #$#1#23%&'(423
5%6)*789':;<= +> +0 ,-23>?
@A +*0ῌ++*.
Iwamori, H. (+332) Transportation of H,O and melting in

237

subduction zones. Earth Planet. Sci. Lett., +0*, 0/ῌ2*.
Jaeger, H.M., Nagel, S.R. and Behringer, R.P. (+330)
Granular solids, liquids, and gases. Rev. Mod. Phys., 02,+,/3ῌ+,1-.
sI J  K ,1 L (+33-) Mt N# 5&'()
&NO= u8vO<w +2.p.
xIyOEPz (+331) {8|}QR~
gh %6 ., S+-S++.
Kelfoun, K. and Druitt, T.H. (,**/) Numerical modelingof the emplacement of Socompa rock avalanche, Chile. J.
Geophys. Res., ++*, B+,,*,.
# (+333) STU?V WNu8vO<w +2.p.
!XW5
Kilburn, C.R. J. (,**.) Fracturing as a quantitative indicator of lava ﬂow dynamics. J. Volcanol. Geotherm. Res.,+-,, ,*3ῌ,,..
Kinjo, T., Ohguchi, K., Yasuoka, K. and Matsumoto, M.
(+333) Computer simulation of ﬂuid phase change :vapor nucleation and bubble formation dynamics.
Comput. Mater. Sci., +., +-2ῌ+.+.
Y  DZ  C[D  IP  \](,***) ^WTU? i_AYj--2p.
:`1a (,**.) +> +0 ,:`bA .
 -32p.
Bcd *D  (+333) %6
< ¡&'()&NO Z¢W£ 2 +,-ῌ+-2.
¤E¥e (,**+) %6¦§W&'()&NO gh
 0 -,*ῌ-,-.
6¨G©fª« (,**.) gm6¬­®o:¯h0!°±RRi¦jk²³´ #$#1#2
3%&'(423 5%6)*789':;<= +>+/ ,-23>?@A -1,ῌ-32.
Kuritani, T. (,**.) Magmatic di#erentiation examinedwith a numerical model considering multicomponent
thermodynamics and momentum, energy and species
transport. Lithos, 1., ++1ῌ+-*.
Laigle, D. and Coussot, P. (+331) Numerical modeling of
mudﬂows. J. Hydraul. Eng., +,-, 0+1ῌ0,-.
Malin, M.C. and Sheridan, M.F. (+32,) Computer-assisted
mapping of pyroclastic surges. Science, ,+1, 0-1ῌ0.*.
Manga, M. and Ventura, G. (,**/) Kinematics and dynamics of lava ﬂows. Special Paper -30, Geological Society of America, Boulder, ,+2p.
Mastin, L.G. (,**+) A simple calculator of ballistic
trajectories for blocks ejected during volcanic eruptions.
USGS Open-File Report ,**+ῌ./.
Mériaux, C. and Lister, J.R. (,**,) Calculation of dike
trajectories from volcanic centers. J. Geophys. Res., +*1B., doi : +*.+*,3/,**+JB***.-0.
Minakami, T. (+3.,) On the distribution of volcanic ejecta.
(Part I.) The distribution of volcanic bombs ejected by
the recent explosions of Asama. Bull. Earthq. Res. Inst.,,*, 0/ῌ3,.
Mitani, N.K., Matuttis, H.-G. and Kadono, T. (,**.)
Density and size segregation in deposits of pyroclastic

238  ¼ ¹

ﬂow. Geophys. Res. Lett., -+, L+/0*0, doi : +*.+*,3/,**.
GL*,*++1.
Miyamoto, H. and Sasaki, S. (+332) Numerical simulationsof ﬂood basalt lava ﬂows : roles of parameters on lava
ﬂow morphologies. J. Geophys. Res., +*-B++, ,1.23ῌ
,1/*,.
 (,***)   1     .2 (+*) .1ῌ/,.
   (+310)  !" ,.1p.
#$%&' (!)#$*+%&, (,**0) "#-"$)./0%&123456ῌ')789():);*+<,0 =-. +1 /0> .?1@A
0--p.
23B4 (+33+) Smoothed Particle CDEF5G67$ HIJ +* ,,3ῌ,-3.
Nagasawa, M. and Kuwahara, K. (+33-) Smoothed particle
simulations of the pyroclastic ﬂow. Int. J. Mod. Phys., B
1, +313ῌ+33/.
Narumi, T., Ohno, Y., Okimoto, N., Koishi, T., Suenaga,
A., Futatsugi, N., Yanai, R., Himeno, R., Fujikawa, S.,
Taiji, M. and Ikei, M. (,**0) A // TFLOPS simulationof amyloid-forming peptides from yeast prion Sup-/ withthe special-purpose computer system MDGRAPE--. Proc.
Supercomputing ,**0.
Neri, A. and Dobran, F. (+33.) Inﬂuence of eruption
parameters on the thermoﬂuid dynamics of collapsing
volcanic columns. J. Geophys. Res., 33B0, ++2--ῌ++2/1.
Niimura, H. (,***) Lattice-gas model with wetness control
for various deformable microstructures. Comput. Phys.
Commun., +,3, +./ῌ+/1.
Nomanbhoy, N. and Satake, K. (+33/) Generation mechanism of tsunamis from the +22- Krakatau eruption.
Geophys. Res. Lett., ,,, /*3ῌ/+,.
Oberhuber, J.M., Herzog, M., Graf, H.-F. and Schwanke,
K. (+332) Volcanic plume simulation on large scales. J.
Volcanol. Geotherm. Res., 21, ,3ῌ/-.
KL 8 (,***) M N
O


 0$9: ,.*p.
Pitman, E.B., Nichita, C.C., Patra, A., Bauer, A., Sheridan,
M. and Bursik, M. (,**-) Computing granular avalanches and landslides. Phys. Fluid, +/, -0-2ῌ-0.0.
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (+33.) Numerical Recipes in C ;P <Q-R=>?S@TA BC *+DEU 02*p.
Ryan, M.P. (+322) The mechanics and three-dimensional
internal structure of active magmatic systems : Kilauea
volcano, Hawaii. J. Geophys. Res., 3-B/, .,+-ῌ.,.2.
VW X (,**.) 6FCDEGH+13, /I  YJKZLYMN1%&1@.* 0-ῌ1+.
SO[\ (,**+) ]^6FCDEPQ_G R`Sa%&1@ /, ,.+ῌ,...
H
Saunders, S. J. (,**/) The possible contribution of circumferential fault intrusion to caldera resurgence. Bull.

Volcanol., 01, /1ῌ1+.
3bM (+331) cdT^eN1f O gU V
GW .2, +*ῌ+/.
Seino, N., Sasaki, H., Sato, J. and Chiba, M. (,**.) Highresolution simulation of volcanic sulfur dioxide dispersion over the Miyake Island. Atmospheric Environment,-2, 1*1-ῌ1*2+.
*+XYhi6j4klg;Z[8mno\ (,**/),+ ]plgq^M NO
krs thi6 +/3p.
Spiegelman, M., Kelemen, P.B. and Aharonov, E. (,**+)
Causes and consequences of ﬂow organization during
melt transport : the reaction inﬁltration instability incompactible media. J. Geophys. Res., +*0B,, ,*0+ῌ,*11.
_"u (+33.) `ZvwxCDEyt56z1t { M NOab cd
Ae +..p.
Sussman, M., Smereka, P. and Osher, S. (+33.) A level set
approach for computing solutions to incompressible twophase ﬂow. J. Comput. Phys., ++., +.0ῌ+/3.
67$\|}~o\ (+33/a) fgh ij 6 k"$"o +2.p.
67$\|}~o\ (+33/b) lm 6k"$"o --0p.
67$\|}~o\ (+33/c) m 6 k
"$"o -+,p.
67$\|}~o\ (+33/d) .M
NOiz5t k"$"o ,**p.
67$\|}~o\ (+33/e)  Jk"$"o ,**p.
nop\Tq (,**0) ^rs
 R


5tCE -  -,, ,*.ῌ,*3.
Tait, S., Jaupart, C. and Vergniolle, S. (+323) Pressure, gas
content and eruption periodicity of a shallow, crystallising magma chamber. Earth Planet. Sci. Lett., 3,, +*1ῌ+,-.
 (,**+)  ¡ ¢yC£¤i i  +/ ,-ῌ-*.
¥  ¦@t4  u§¨  -Wv©  wx y(,**/) SPH CDE^z #$#$%&{%|}ª%& «^z z5t¬ -. +0 /0%&.?1@A ,3.ῌ,3/.
o ­ (,**-) i 
vw® ;Z ~ +-+/*ῌ+0,.
o ­GuMu (,**/) ¯t°±²³´µ¶G·.27$ #$#$%&{%|}ª%& «^z z5t¬ -. +0 /0%&.?1@A ,.,ῌ,./.
Takahashi, T. (,**+) Mechanics and simulation of snow
avalanches, pyroclastic ﬂows and debris ﬂows. In Particulate Gravity Currents (McCa#rey, W.D., Kneller, B.C.
and Peakall, J. eds), ++ῌ.-. Special Publication Number-+ of the Int. Ass. Sediment., Blackwell Science, Oxford.
¸ K ¹º (+32.)  
 "!)%/1 ,1B, .01ῌ.2/.
¸ K ¹ºyO (+331) ^»&¶h·¸¹ºd»¬ef¼( )*
  /*,*ῌ,/.
       !" (+33-) #$% +33+ῌ
3, &&'( )*
+,-. .. ,/ῌ/..
/01 (+332) 234 5678
9:;&&<=5 >? +22p.
Tanaka, H.L. (+33.) Development of a prediction scheme
for volcanic ash fall from Redoubt volcano, Alaska.
Proc. First International Symposium on Volcanic Ashand Aviation Safety. USGS Bull., ,*.1, ,2-ῌ,3+.
Tanaka, H.L. and Yamamoto, K. (,**,) Numerical simulation of volcanic plume dispersal from Usu volcano in
Japan on -+ March ,*** using PUFF model. Earth
Planets Space, /., 1.-ῌ1/,.
 !B"#  /$C  D%&
1@  A
(+33.) &E F'
5 #$(G% +33+  0 . 2 )5 & -3 ,/1ῌ,00.
The Earth Simulator Center (,**/) Annual report of the
Earth Simulator Center April ,**.-March ,**/. The
Earth Simulator Center, -/,p.
Thompson, J.F., Warsi, Z.U.A. and Mastin, C.W. (+33.)
F'H7IJKLMN* OP Q +,-RS -/,p.
Tinti, S., Bortolucci, E. and Armigliato, A. (+333) Numerical simulation of the landslide-induced tsunami of +322
on Vulcano Island, Italy. Bull. Volcanol., 0+, +,+ῌ+-1.
Todesco, M., Neri, A., Ongaro, T.E., Papale, P., Macedonio,
G., Santacroce, R. and Longo, A. (,**,) Pyroclastic
ﬂow hazard assessment at Vesuvius (Italy) by using
numerical modeling. I. Large-scale dynamics. Bull.
Volcanol., 0., +//ῌ+11.
TU.@VD/ "WX0YZ[ (,**0) 1\2] 3^_`abcde:;f4gh
&i5j )63k  ,**0 7lm1no8
pq ,++.
96:/rs;t  (+333) H73<=H

239

7uvwx =5yz{F'< |= ([}~ +1.p.
>1"?@ (,**/) 8AJ b
C +3
B&F'
F'<  noDq +2ῌ+3>EFE (+33*) G<
H I 0/ -,+ῌ.++.
5:;L J (,**-) K7
7|=<=5 >? ..0p.
Valentine, G.A. and Wohletz, K.H. (+323) Numericalmodels of Plinian eruption columns and pyroclastic
ﬂows. J. Geophys. Res., 3.B,, +201ῌ+221.
Wadge, G., Jackson, P., Bower, S.M., Woods, A.W. andCalder, E. (+332) Computer simulations of pyroclastic
ﬂows from dome collapse. Geophys. Res. Lett., ,/, -011ῌ
-02*.
White, J.D.L., Smellie, J.L. and Clague, D.A. (,**-) Explosive subaqueous volcanism. Geophysical Monograph,+.*, American Geophysical Union, Washington DC, -13
p.
Wohletz, K.H., McGetchin, T.R., Sandford, M.T. andJones, E.M. (+32.) Hydrodynamic aspects of calderaforming eruptions : numerical models. J. Geophys. Res.,
23B+*, 2,03ῌ2,2/.
MN DO (+322) FORTRAN & C  
¡=PO )¢£¤yQ~ ,11p.
MN R¥¦§J (+33,) ¨©( 
ST Uª«V +3,p.
MK (,**+) ¨©( =¦¬4
nW~
-0*p.
MK­XY Z (+332) [®D¯=¬ Uª«V +,2p.
B°\]±6^_16¥²³`´µ/
(+33*) aF'
µ£ bcq-. -3+ῌ-30.
Young, P. and Wadge, G. (+33*) FLOWFRONT : simulation of a lava ﬂow. Computer & Geosciences, +0, ++1+ῌ
++3+.