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ῒΐ /, (,**1) . ,,+,-3 腑腗腕腓腅腄腖腔腁腒腙腂腇腆 腘腚腃腈腐腋腍腀腊腉腌腍腏腀腉腎腐 ,**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 +ῐ῎ῑ῏ 臏臫膻膴臃腐膾膈腶膂膚膐膔腃膈膃 膓膔膘腃膃膕膚腨臵臔腯膵腦腱腴臵膌腃膈腧腯腘腦膸腠腒膰膹腧臝腦致腓臨腧臹腣腗腡腊腲腰腴臒膿膕膣腑腥膱腷膡腘腴腱腌腦腥腞腡腋 臏臫膻腑膅腨臎腠腳腦臚腔腡腎腳腛腵腦臡 腶腚腡膏膖腾膋腺腦腬臏臫臹腧膭腸腢 腋腴膺腦腍膬膢腆膔膰膿腙腴臹腣腗腡膂膚膐膔腃膈膃膓膔膘腃膃膕膚腐膤臐腦腥腞腡腎腳腴膪膉膛腨膰腦膸腠腋腡臕臮臮腧臀腙腴腥膅膁腃膗腏腲腤腌腗腧臘臦腷臏臫 腗腡臊膦腧腒腰腷膪腙腴腵膗膅膁腃膗腪腢膹腦腶腜腴 腇腡+33- ; 腇腷,**- ; 膤腚,**+腅腁 膂膚膐膔腃膈膃膓膔膘腃膃膕膚腨腪腁腥臋腳 腗臏臫腐膎膫腥臖腷臷腥腦腆腣腗腡膈腶腗腡腑腜腗腏腗臤臈腢腨臧腥膔膰膒膙膆膅腐腫臡腌臖腦腟腋腡腮腕膺腥膃膓膔膘腃膃膕膚腐膤腦腥腳膦膪 腉膜腲腵腴腱腌腦腥腞腜腕腧腜腭腕腵腪腢腨 腐腭腐臣腝腞腜腣膨腥臖腧臒膿腦膃膓膔膘腃 膃膕膚腐膯膪腖腵臭腭腡腋腴 腛膱腳膇膑膍腼腽腹 自臇膢膪腏腎臂膽膩,**/ ; 腐腭膲腥膶臻膜膟膩+33/a ; The Earth Simulator Center, ,**/腅腁 膧臩膧腦膶腙腴膂膚膐膔腃膈膃膓膔膘腃膃膕膚腨 膬膮腢腨腳腔腸腝腐膂膡腢腨腄腐腦臗腲腵腡 腋腜腕腧腱腌腥臄腷腤膆腙腴腜腭膧臩臒膿臶腐腐腭臏臫腧臍臔腐膟膑腢膕膣腧臒膿臶腣臁腗腡膧臩 膃膓膔膘腃膃膕膚腦臸腳腬臲腫腐腥腖腵腴腱腌腦腥腞 腡腋腴腍腩膥膰膼腀腋臅膻臝腧臏臫膥膰膼腾腱臒膿膭膈腏腎至臇腢腨膧臩臒膿臶腣臕臮臛膰 腧臒膿臶腐臂腗腜 膧臩膃膲腥膃膓膔膘腃膃膕膚腣膴 臃膠臆膧腞腧膭腣腋腌膒膙膄腽膀膍腐 ,**+ ,**. 腪腢臵臰腖腵腯膧腼膀膲腵腥腤腧膃 膓膔膘腃膃膕膚腐臟腶腵腜 腍腩腹腷,**. ; Hidaka et al., ,**/腅腁 膗膒膥膰腧膥膰臒膿膌膛腃腾腱膵膝臒 膧臩膇膈腧膉腻膎膓膊膀膅腇腄,**,,**0 膄腸腢腮腢膕膣腧臒膿臶腏腲腐腣腒腧臂腳臙 -*/***0 臓腟腒腩臯-+ 臥膥膰膼臒膿National Research Institute for Earth Science and Disaster Prevention -+ Tennodai, Tsukuba, Ibaraki -*/***0, Japan. Corresponding author : Yasuhiro Ishimine e-mail : [email protected]
19

Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

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Page 1: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

� �� ��� � /,� (,**1)

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�,**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

+� � � �� � �������� �������

�������� !"#��$% �&��' �(�)��(*+��',��-.�/'0�1�2345%67��8�9:�;<=>%$?�:@2A%B � ����C���D���E2FG HI�JKL2MNOPQ��R� 0�'STU�V�W8A%BX�� !"'#�Y"<$7Z%0%1�2���������������&[\�:@2FGH''()]�*^+_�(*A2)^T�^'`,<-�Z%.a�:bc�de4/f?�'0gh(<� �2ij'12k3<l4Z%56_�bc�dm87n�Ko% ��8T9 +33- ; �: ,**- ; ;< ,**+B��������������� p= >?:qG@�� �AB:Y"<r:C"1�2��29oB�e� s�8� Dt:#�uvwb�ExJ?Y"�yA2VFG:���������[��:G H(:IJ�K4I%$?�:@oB z'o{ zIm8�

LMl4�|N}@o7O:Y"'67� ���������P(~I�{2A% �QR�(S���������(T���� ,**/ ; LMUV+_W����+33/a ; The Earth Simulator Center, ,**/B��X���YZ%�����������������8�Z��[W}� ���\8�]L��4I2AoB z'$?:^�<_`Z%o{ ��67��LM� '�!�a�:9��'67�1�b�2������������GcR�x�:~I%$?�:@2A%B d�� �_ ef¡�,'� �_ e¢(£gh67ST�¤�8� ��67�1)^+¥_'67���+�o ¦��iUV��������1��§¨-�0�'S© 1A?uvª�«�� ,**+�e4 ,**.�m8 ¬~I j­U"�k\UI:f'���������®KIo �d��l: ,**. ; Hidaka

et al., ,**/B 6m�_n'�_67opq¯ghr°67 ¦��s'±²³�´«b© �,**,�,**0�t 8V9��'67�e4L7+'�+<K2 µu:vG¶

�·-*/�***0 ¸w¹y+�º5»x -�+y¼�_ e67zNational Research Institute for Earth Science and

Disaster Prevention

-�+ Tennodai, Tsukuba, Ibaraki -*/�***0, Japan.

Corresponding author : Yasuhiro Ishimine

e-mail : [email protected]

Page 2: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

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Page 3: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

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��� D�� w��|�� O!P�L����� }������|�� g��h Gi~�GI�D^�]NG*�9���_G6KL� ������|�������1 g��h GiT5�������}������cde�cf�1���DI��A� ,�������� �:�� ��1� "#F�G����� g"#��h GiT5�!"���� F�4��� C�"#��V����� "#�������B� Z� +\� J0��1� F�G��� #�J*L1C5��E�J��]NG��*��C�]N���?0*���� "#�������B� Z� ,\�"#�� ��������1� "#��G|���� F�4���$[T� � + (a)�1� ����IU�� +� ,� -� �� ����IU�� +� ,� -� �G%� &A� C��' Z��'D�1�'GiT5�\ ��(=�> |��G*� f (+, +), f (+, ,), f (+, -)� ��?G�^)��� _�*�1� � M��A������+ ,¡*�!G:��¢5�_G6K!� -<"#�1��' ��V�£.4���6����B�� �*� ¤¥<�"#�1� �<�(¦��§�"#��J

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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.

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Page 4: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

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Fig. ,. Schematic illustrations of a substance repre-

sented 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 the

dashed line in (b), which is described by the

superposition of Gaussian distributions to have

continuous values.

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������������� ��� � ����������������������� ����� �������� ������������������ � ������������������ ��������� ��!"� �#���$%�����&'����(��)�*���� ��)+,-.! �/���"#�)0$�%&�1� ��23�4')*(�)5/���*67+, 8,�--9 ).��Kuritani (,**.)�:�;</�1�����0 +=>�1/����2?&��2�@����+3�4&ABCDEAFG 8,�3-9 ).��*(�H�!�� 8I5'6J� +331�:9��K��L�78)MN/� #��GOP�Q &9/��:R� ;<)= ��STOUVWTXYO���)>Z[�\? 8,�3-9 �2��@A�;<�:�H!�� (Iitaka et al. ,**.)�

-�. �����������#����� ����������B]�^C�D��E_��� ����FGH�`<)Ia���JK� ����LFbM����/0c������23�4'�*(���*6&9, 8,�.- ; dN'OP� ,**/9 �ef&9, 8,�0- ; Dahm, ,*** ; Meriaux

and Lister, ,**,9 �Q.���� L�� `<�RS��g���T��h���*(��� *6&9,(Ryan, +322 ; Saunders, ,**/)�ef&9, (Cayol and

Cornet, +331 ; Gudmundsson and Brenner, ,**/)�U.�)5�����#����� ����i.! �/����2�V�� �#��������� L�!W�X9�:�Y%jk�$a� ����I.�l4�m��Z[\il)#n/i]/��(^����1 (Carroll

and Holloway, +33. ; Tait et al., +323)� o_`o�p��������ab����� ��(^��qT +�"#��r)s/0c���� ��� qT +�. ��tc�+d�u� . �+�qT +�e%�Hf��T�gh�� ��iv��� Y^�L��Y^wEx�y /�3jzp���T{YP�`o��� . ��i]�k�j ��LL l)m%/� ���)n|�Eo�4' 8}~��G�EAFG9 ���� ���g� n|��������qT +//��oJ��`^���ab�`o�1�b]4'�@���Kinjo et al. (+333)�=p'q

(,**/)�:� Lennard-JonesS�GA�P)r��+3�4&ABCDEAFG 8,�3-9 ))5�$a����

���"#������� 8s -9� Mt�i]� l'v1��������)�����\?�� fGABCDEAFG 8,�+.-9 ��u���.//�av�� wx�o_4'/jz��23���\?t�yM��� � 4z���L�H!����23�1� ����Eo�{��m����|�:�o_;<�}&��E����0~������P)Q��z��h�����/�3��Z�����23��Z~���P�24'�*��4�m%����

-�/ ���� ���ab�o_`o�0���� �����/k:�o_��+���Y� 8,B��EOP�#9 �Eo�� �������E����������� ���qT +�������� � �3/qT���Z1/���Hf���J�-i� �1�oJ��`^����� o_`��1� o_`�������*67+, 8,�--9 �������ABCDEAFG��0�)5����`�ABCDEAFG�� m�<�2��� M�� ,

���+%�� Z@�� jz���\?�� 8LF�����V�� +**�V|�9 )����`����Q�)����4�� `������Y B¡¢T��*)� �/)</����1 8s .9� �3Z@�� ���+��:�wA�E{/���)}7��� `��B]��������b������|)� jz ¡�£¤¢)�5jk���P�\?�{Y¥�1�£¤�{Y¥��� ����)���i 8o_qT/Mi��vi19 ��=>�o_��Mt�¥¦���¦§�:)� §¨���P��23/�¨��©�� ��!"� o_��©@ªª«P¬E�2��Mi�ª«¬)­��� m��g� ¥4����M®­�JK��bh�/�323�Z®�¥V¯T)� ���%¯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,�+,-9 �1� ������P)bS�µ�;<�0�� bT��� 8Clarke et al., ,**, ;

Neri and Dobran, +33. ; Valentine and Wohletz, +323�:9����0����`����¥4�´+�b���¶��`�µ���� `�µ¶_/·u4'�­��Mi2a�}��-i� �1�oo�/����G�¸���M���+¹{��º·��¸/�����

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Page 11: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

���� �������� ����� Oberhuber

et al. (+332)��������������������Dartevelle et al. (,**.)� ������� �!"���#$���%&'( (,**0))�� �*�+ ,-�.���/�01 ���� �23�456���7�8� 9,�.:; <=>?@<AB���(%� (+33.)�C�)D�/E61FG�� C23�HIJ%KL�30MN�OP56QRS T� ���U .VW.�XYZ@[���\]^� _\`��K�56�H�ab� !c d6C� �eRBfg3061 h�"#� i$�U�j% k�3T&l)mn'(o)�3� �p 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��QRS�OPT� � ��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� h�I.�<=>?@<AB ��M�=>��3061

� .1 ���H�<=>?@<AB� 9�? @¡>�;1 ¢£¤¥ +33+A��vB�� E6C 2¦ kg�s��§D OP���H�i$E#¨��/� � ��©ª +.**F«�G��§H�¬I'D 9­�§H®�­�§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.

� -1 '�JKy<=>?@<AB C6�L4³�OP� 9´µMN¡>�;1 ,³'¶�·bOP C6�L�4³N�OP��/� � QRS5T0��U VlHS5¸0��I¹§�3� �Lv)2306G�¨�3061

Fig. -. An example of Molecular Dynamics Simula-

tion for bubble nucleation (Courtesy of T. Kinjo).

The time evolution of bubble nucleation due to

instantaneous expansion was investigated numeri-

cally. A bubble with several solute molecules (red)

appeared in the surrounding solvent molecules

(white).

��~�`�º»InWfg6�G)¼B¢>@Q<=>?@<AB 231

Page 12: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

����������� ���� ��� ������������������������� !"�#$ �%&� '�(� (,**,)) Seino et al.

(,**.)�� ,*** *����� !��+"�#��,�-���./���0���#$ 1�(� (+333)

2� 3�����������4#���5����6� 7#�8� !"#9 $:;�<��=���������#%��#$

-�0 ����&�>?�������'�2� ���2()�*+��+ @ABCD� ,���EF GH�IJ"�# K-��#$ L.B/0� ��E�1M��2 !)3(4�A#N5�67�� �2 8��OP9�A# �Q���,���#$ ����� :;<BP9�A#=RB�+ @��STF �IUV��0��2��WRB�$��ST�XY�>?���2� Z�@A�BHB�!C�/��P9A#DE�P9 [B��F�0��'� !G[!"\] @Minakami, +3.,B^F� H1W2���IJW_;`K�A#abcde�fg+"�# (Mastin, ,**+)$ � �� =RB�+�h0�=R� L%!"# i�jb�klM��m �4QBV����� �+ �2�2nN��OP�QoWR#4QBRS���2JG�T+"�B�4QWp#$���� qU�rcr��sR B���A# ituvM��m J�2 iVS�Wm w&"#�=v��RS<Bxy!"�B�$ z�4QB��STB^��+�IUV��0��2� SPHJ @,�++XF ����RS���������Y{Wp#$ �%&� Z[(� (,**/)�����\��4�S]�>�A#���������� C� Z�@A�{|�OP�^[_8&� Y�B`a�b!"# }c+"#$

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=v���B#�"��R�zA (Gri$ths, ,*** ;

Manga and Ventura, ,**/)$ z"!��9�=v���A#xy2�����G�� ��'�2� ��)#9��|���B0���� ^[0C:�����Wp# (Hon et al., +33. ; Kilburn, ,**.)$VUW2� VS���A#���������� �^2� H=�f�M�qVJ�2����< ���Wp#$ &��7�4Q�� �9�=v����A#�,|}2���,�tuB�8� z�=va�����2��<��a�B�9��^[_J"�#$ �YB�ab��W����,�G[!"�#�� '��/0� �"��������,���)����B^�`KA# ,����������#$xy��'��2�Y��)J @,�-XF J�2Y���J @,�/XF ���� ,�����Wp#$ z"!� ,

�����2� ����#�5M��4�� +!�,��=�+"#$ ��2� �������/W��"��+)������R ��%#P9�<B-M,�� @ �r¡¢£¤���F Wp#$ Q��2������¥�)¦����§Oz,A#{|�L����<B��� @¨v©�£¤���F Wp#$ � �2�¡ª(� (+32.)�Miyamoto and Sasaki (+332)� Young

and Wadge (+33*)B^�p#$ « �2� ¢+��7�����z,�*+� �Qx£1¤�����¥�£�5M������'� @Costa and Macedonio,

,**/ ; �¬(�� +33*F$ z�� � ­¦������(Favalli et al. ,**/))� ®�¯�jrj�J @,�+-XF�O��G[�� (Crisci et al., +333)p#$ H1W2�VS��T§ !��(°,��"���B#ab®��^[_�G -����)���g�+"�#@Hidaka et al., ,**/ ; ¨ /F$��B��&��".�#V� �Q�E !±#

� VS� � �X*�W©ªA#«¡�� �e�2���� �²¬A#hD�­��#$ ���8� RS����-M,�¤E�'�$n��®³�B���=RBRS´���O+:#µ��¶�E�L��Y���J @,�/XF ��������'���²¬��n~Wp#$ z�E2� ¯°)±�B^� ��*·��6�4#��&��"��Wp#$ ���8� z"!�V��J 8����#²¸p# (Denlinger

and Iverson, ,**+ ; Takahashi, ,**+)$ Beven(,**+)� ³�(� (+323)B^��²��´µ¶·L�B#$

-�2 ������ �����«¡���A#xyW2� �XW¸¹��¥�£�5M�Y��)J @,�-XF W���,�����'�@Laigle and Coussot, +331 ; º¹(�¬� ,*** ; Z»(º

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Page 13: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

�� +32.���� �������� ������������� ����������� ������������ ��� ����� �!" #$�%�&�'���()��!�� &�*+� �,��-./0� &1� ����������0!�23/��������405��6 4�7��� ��� !��"#8�$9��� :%&'�&�(7'���)�;���6��)<���� =>*���� �?@� �!�AB���C��+,����-.�/D&�EFGH�01�2I� J�K� �L�3M04�56�NOO���7��� !�P8�2�5��� 6��Q?����R9:R�;<S�=I<>0?T��U@�9A� VAW�X���>���� YZ[2\Y]^�J_BC ��`D��"���� (Heinrich et al., ,**+ ;

Kelfoun and Druitt, ,**/ ; Pitman et al., ,**-)� NX�����0�� abIEF��0cd"��4�4;��= �>N�"��,� AW�X�0�e=f'�4�gG����Q?�����H0-./h����?T�� ON� AW�X����9�i�4��!�B���O�O;�e=&����"�IJ��� jK1$D V,�+*L� ���7'�k7&�Ml>m*���� VCampbell et al., +33/ ; NOnPQ� +33*����

AW�X��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��

-�3 ���R|��� AW�X��BC�� }~�V�X�<.��;�u[0�����7'05�� �!�R9AB�<.I\ AB�+,������D� ��X]^��� M_R|`�a�b�;�R9�HI�~������C��c�e=�&� ��\�]^� =�'�"����H��"05�� u�05�6�>7'�de������Q?������R|��� S?f�r�� �gh�st�N�� 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

and Kokelaar, ,**,)� � � � \ 7'=� wx������C��-./h��"����� ���� �� 2� ��X� � ��\�� �y�^8�� �+�=,X8 ���m;����R|�\� z{YZ[2\Y]^�q>����m;

��� �� Neri����� �/\E05� (Dobran

et al., +33. ; Giordano and Dobran, +33. ; Todesco et al.,

,**,)�|���3H��R9}~ ����8�� �H¡��¢&�N�� 7(��<��R|�\� ���£�� 4�¤¥�¦_&=�� §X���¨����� C��©�=�ª�������� � \� R|�\�=�b���S�&����¨�«��NIshimine (,**/)I¬F^��n�2­HR90 :R �® ��MlN Cordoba (,**/)���5����¯N0�� ������BC �4U������ ,�° z{-./0� �X]^�:%&�����K05� VItoh et al., ,*** ; u±n\� +331�� BC -./��No²0 �� �>5� (Wadge et al.,

+332)� ��n9O (+33.)0�� �X��\� e=��l*zN-./��������� |������f0�1���4��\�]^ e=�����(7'�5O�O�k70!�����6 \�>� 4�Y^E/���/�\¬\^-./VR|���³���´���/�\�� �D�;�

� /� �A� YZ[2\Y]^� V�Oµ���c�� ��9� -. R¶=� ,** m-�s0�A��¡&��¢i�����N� 0� <£ ·-I¸¤ ¤¥�¥8���¹¦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 hetero-

geneity.

R9��® »��³§"���C�¬^¼[\�YZ[2\Y]^ 233

Page 14: Overview of Diverse Computer Simulations and their Potential … Overview of Diverse Computer Simulations and their Potential Contribution to Volcanology Yasuhiro ISHIMINE This paper

������������� ������������������ ����������� � �Malin and Sheridan, +32, ; ���� +33-� ! ����� �,�+*�� ���"#�������$�"� � (Mitani et al., ,**.) SPH� �,�++�� ���"� � (Nagasawa and Kuwahara, +33-) %&�'�(

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