䝋䝙䝑䜽䝤䞊䝮᥎⟬䛾䛯䜑䛾㧗⢭ᗘ㏆ഐሙᅽ ຊἼᙧ᥎⟬ᢏ⾡䛻㛵䛩䜛◊✲䠄䛭䛾䠎䠅

(1)

䝋䝙䝑䜽䝤䞊䝮᥎⟬䛾䛯䜑䛾㧗⢭ᗘ㏆ഐሙᅽ ຊἼᙧ᥎⟬ᢏ⾡䛻㛵䛩䜛◊✲䠄䛭䛾䠎䠅

◊✲┠ⓗ

ཬ䜃ෆᐜ

ᮏጤク◊✲䛿䠈Ᏹᐂ⯟✵◊✲㛤Ⓨᶵᵓ ⯟✵䝥䝻䜾䝷䝮䜾䝹䞊䝥䛜㐍䜑䜛㟼⢔㉸㡢㏿ᶵᢏ⾡䛾◊✲㛤Ⓨ䛷ᚲせ䛸䛺䜛䠈䝋䝙䝑䜽䝤䞊䝮᥎⟬ᢏ

⾡䛾䛖䛱Ẽయ㏆ഐሙ䛾ᅽຊἼᙧ䜢㧗⢭ᗘ䛻᥎⟬䛩䜛ᢏ⾡䛾⋓ᚓ䜢┠ⓗ

䛸䛧䠈᱁Ꮚ⣽ศ໬䛻ᇶ䛵䛟ゎ㐺ྜ᱁Ꮚἲ䛾㛤Ⓨ䜢⾜䛖

ᮾ໭኱Ꮫ኱Ꮫ㝔ᕤᏛ◊✲⛉⯟✵ᏱᐂᕤᏛᑓᨷ

୰ᶫ䞉బ䚻ᮌ◊✲ᐊ

◊✲ᢸᙜ⪅䠖

䕿኱ᮌ⿱௓䠄ಟኈᏛ⏕䠅䠈బ䚻ᮌ኱㍜䠄ຓᩍ䠅䠈୰ᶫ࿴༤䠄ᩍᤵ䠅

Outline

1. ⫼ᬒ䞉┠ⓗ

2. ゎ㐺ྜ⣽ศ໬ἲᴫせ

¾

ᩘ್ィ⟬ἲ

¾

⣽ศ໬ᣦᶆ(Shock Function)

¾

⣽ศ໬ᡭἲ

¾

ゎᯒ౛

3. ᚑ᮶䛾ᡭἲ䛾ၥ㢟Ⅼ䛸ᑐ⟇

¾

ၥ㢟Ⅼ

¾

㎶㛗䜢⪃៖䛧䛯䝣䜱䝹䝍䝸䞁䜾

¾

ẚ㍑ゎᯒ

4. ⤖ゝ䞉௒ᚋ䛾ㄢ㢟

(2)

⫼ᬒ

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 3

` ㉸㡢㏿᪑ᐈᶵ䛻䛚䛡䜛㦁㡢ၥ㢟

z

ᶵయ䛛䜙Ⓨ⏕䛩䜛䝋䝙䝑䜽䝤䞊䝮䛾పῶ䛜ᚲ㡲

z

ᶵయ䛾ప䝤䞊䝮タィ䞉ホ౯䛻䛿䚸ᆅୖ䛷䛾䝋䝙䝑䜽䝤䞊䝮䛾 ṇ☜䛺᥎⟬䛜ᚲせ

` ᆅୖ䛷䛾䝋䝙䝑䜽䝤䞊䝮᥎⟬

¾

ఏ᧛ゎᯒ䛻䜘䜛᥎⟬ἲ

z

㏆ഐሙ䠖 ᶵయ㏆ഐᅽຊἼᙧ

z

୰㛫ሙ䠖䝋䝙䝑䜽䝤䞊䝮䛾ఏ᧛

z

㐲᪉ሙ䠖 ኱Ẽ஘ὶ䛾ᙳ㡪

୰ 㛫 ሙ

㏆ഐሙ

୰㛫ሙ

㐲᪉ሙ

⫼ᬒ

` ㏆ഐሙᅽຊἼᙧ᥎⟬䛻䛚䛡䜛せồ

z

ᅽຊἼᙧ⢭ᗘྥୖ

z

ᐇ⏝ⓗ䛺ィ⟬䝁䝇䝖

z

ᐇᶵ」㞧ᙧ≧䜈䛾ᑐᛂ

{

ຠ⋡䛾Ⰻ䛔᱁ᏊⅬ㓄⨨䛾ᚲせᛶ

{

㉸㡢㏿ᇦ䛷䛿≀⌮㔞䛾ᛴ⃭䛺ኚ໬䜢䜒䛯䜙䛩⾪ᧁἼ䛜ᨭ㓄ⓗ

¾

㠀ᵓ㐀᱁Ꮚ䛻䜘䜛⾪ᧁἼ㡿ᇦ䜢୰ᚰ䛸䛧䛯

ゎ㐺ྜ⣽ศ໬ἲ

(3)

┠ⓗ

` 㠀ᵓ㐀᱁Ꮚゎ㐺ྜ᱁Ꮚ⣽ศ໬ἲ䛻䜘䜛

㏆ഐሙᅽຊἼᙧ䛾㧗⢭ᗘ᥎⟬ᡭἲ䛾㛤Ⓨ

z

⾪ᧁἼྠᐃ䛻㛗䛡䛯ᣦᶆ䛸䛧䛶Shock Function䛾ᑟධ

z

୕ḟඖⓗ䛻⾪ᧁἼ䜢ᤊ䛘䛯㝿䛾ᅽຊἼᙧ䜈䛾ᙳ㡪䛾᳨ド

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 5

NEXST1 ԥ P

ྍど໬ᅗ(ᑐ⛠㠃,

R =3)

ึᮇ᱁Ꮚ

^{⣽ศ໬(Zӌ0.5)} ^{⣽ศ໬(Zӌ6.0)}

ᩘ್ィ⟬ἲ

` TAS-code (Tohoku university Aerodynamic Simulation code)

`

୕ḟඖ㠀ᵓ㐀ὶయ䝋䝹䝞䞊

ᨭ㓄᪉⛬ᘧ ୕ḟඖEuler᪉⛬ᘧ

✵㛫㞳ᩓ໬ἲ 䝉䝹⠇Ⅼ᭷㝈య✚ἲ

ὶ᮰ホ౯

HLLEWἲ

᫬㛫✚ศ

LU-SGS㝜ゎἲ

(4)

! 1

shock

f f _shock 1

⣽ศ໬ᣦᶆ(Shock Function)

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 7

` ⾪ᧁἼྠᐃ䛻㛗䛡䛯Shock Function䛾ᑟධ

z

⾪ᧁἼ㠃௜㏆䛻䛚䛔䛶

Ἴ㠃䛻ᑐ䛧ᆶ┤䛺㏿ᗘᡂศV

_n

䛜㡢㏿䜢䜎䛯䛠ᛶ㉁䜢฼⏝

a M V

f

p V p

V

n n shock

n

x &

&

ᅽຊ໙㓄࣋ࢡࢺࣝ

㡢㏿

㏿ᗘ࣋ࢡࢺࣝ

: :

:

p a V

&

p &

V &

) Shock

( p & A

V & n

Shock ) 1 ( f _shock

⩼㠃ୖ䛾⾪ᧁἼ㡿ᇦྍど໬ᅗ

(M=0.84䠈f _shock =1➼್㠃)

㉸㡢㏿ᇦୗ䛷䛾ᩘ್ㄗᕪ䛾ᙳ㡪

` ㉸㡢㏿ᇦ䛷䛿ᩘ್ㄗᕪ䛜⾪ᧁἼ㠃䛾ྠᐃ䛻ᙳ㡪

z f _shock

䛾䜏䛷䛾ྠᐃ䛜ᅔ㞴

` ᅽຊ໙㓄䝣䜱䝹䝍䞊䛾ᑟධ

¾

ᅽຊ໙㓄䛜㜈್䜘䜚኱䛝䛔㡿ᇦ䛷ุᐃ䜢⾜䛔,ᩘ್ㄗᕪ䜢㝖ཤ

E thr

p t

&

E _thr :䝣䜱䝹䝍䞊㜈್(ᐃᩘ)

䝣䜱䝹䝍䝸䞁䜾䛺䛧䝣䜱䝹䝍䝸䞁䜾䛒䜚(E

_thr =0.01)

f _shock

䛾ྍど໬ᅗ(M=1.41, ᑐ⛠㠃)

(5)

⣽ศ໬ᡭἲ

` Bisection䜰䝹䝂䝸䝈䝮䛻䜘䜛ศ๭

`

ᅄ㠃య䛾᭱㛗㎶䛾୰Ⅼ䛷ศ๭

` ෌ィ⟬᫬䛾཰᮰ᛶ䛾ᨵၿ

`

⣽ศ໬ᚋ䛾᱁Ꮚ䛻䚸

⣽ศ໬๓䛾≀⌮㔞䜢ෆᤄ

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 9 Shock Function 䛻䜘䜛

⣽ศ໬ุᐃ䛸⣽ศ໬䛾ᐇ⾜

⣽ศ໬ᚋ䛾᱁Ꮚ䛻

⣽ศ໬๓䛾≀⌮㔞䜢ෆᤄ

෌ᗘ䚸ᐃᖖゎ䛾ゎᯒ ᱁ᏊⅬᩘ䛾ቑຍ䛜䛒䜛䛛

ึᮇ᱁Ꮚ䛻䛶 ᐃᖖゎ䛾ゎᯒ

⤊஢

Yes

No

h/L=5.0 h/L=3.0

ԥpศᕸ(ᑐ⛠㠃)

h/L=5.0 h/L=3.0

ึᮇ᱁Ꮚ(ᑐ⛠㠃)

` ゎᯒᑐ㇟

z ㍈ᑐ⛠≀య

z A(x)=0.02x (0ӌxӌl)

z

䡈

䠙2in.

` ゎᯒ᮲௳

` ึᮇ᱁ᏊⅬᩘ䠖⣙55୓Ⅼ

` 䝬䝑䝝ᩘ 䠖1.41

` ㏄ゅ䠖0㼻

` ᅽຊἼᙧྲྀᚓ఩⨨

z ᑐ⛠㠃ୖ

z h/L=3.0䠈5.0 (ᐇ㦂್)

ゎᯒᑐ㇟䛸ゎᯒ᮲௳

L=1 3L (䝇䝔䜱䞁䜾㒊䜢ᶍᨃ)

(6)

` Shock Function

z ᅽຊ໙㓄᪉ྥ䛾㏿ᗘᡂศ䜢⏝䛔䜛䛯䜑

್䛜Ᏻᐃ

` ᅽຊ໙㓄䛾⤯ᑐ್

z ῶ⾶䛾ᙳ㡪䛻䜘䜚,㐲᪉䛷䛿ኚື㔞䛜ῶᑡ

h/L=0.5 h/L=1.0

ᣦᶆ䛾ឤᗘẚ㍑

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 11

ึᮇ᱁Ꮚ䛻䛚䛡䜛ԥpศᕸ (ᑐ⛠㠃)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-1.5 -1 -0.5 0 0.5 1 1.5

0 1 2 3

P res su re G ra d ie n t[- ]

S h oc k F u n ct io n [- ]

x h/L=0.5

ShockFunc PressureGrad

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-1.5 -1 -0.5 0 0.5 1 1.5

0 1 2 3

P res su re G rad ie n t[ -]

Sho ck F unc ti on [- ]

x h/L=1.0

ShockFunc PressureGrad

ĺᗈ⠊ᅖ䛷䛾ุᐃ䛷䛿䠈Shock Function䛜᭷ຠ

Case1 Case2

Case3 Case4

⣽ศ໬㡿ᇦཬ䜃᮲௳

` ┤᪉య䛾⣽ศ໬㡿ᇦ

` ⣽ศ໬ᑐ㇟䛾ุᐃ

z

⣽ศ໬㡿ᇦෆ

z

ᅄ㠃య䛾᭱㛗㎶䠚ศ๭㝈ᗘ

z

௨ୖ䜢‶䛯䛩ᅄ㠃య

Case1 Case2 Case3 Case4

ᅽຊ໙㓄䝣䜱䝹䝍䞊

⣽ศ໬㜈್

ศ๭㝈ᗘ

0䍺z䍺0.1 0䍺z䍺0.5 0䍺z䍺1.0 0䍺z 䍺2.0

⣽ศ໬㡿ᇦ

E thr =0.01

|f shock |䍻1(⭾ᙇ㡿ᇦ䜢⪃៖)

0.05 0䍺x 䍺10 -6䍺y䍺0

t 1

t

p & E _thr f _shock

(7)

⤖ᯝ(᱁Ꮚ)

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 13

Case1(0ӌzӌ0.1) Case4(0ӌzӌ2.0)

ึᮇ᱁Ꮚ

ึᮇ᱁Ꮚ Case1 Case2 Case3 Case4

⣽ศ໬䞉෌ィ⟬ᅇᩘ - 12 13 15 18

᱁ᏊⅬᩘ ⣙㻡㻡୓Ⅼ ⣙㻡㻤୓Ⅼ ⣙㻣㻡୓Ⅼ ⣙㻥㻠୓Ⅼ ⣙㻝㻟㻜୓Ⅼ

⣽ศ໬㡿ᇦ ⊃䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷䚷ᗈ

Case2(0ӌzӌ0.5) Case3(0ӌzӌ1.0)

ᑐ㇟㠃ཬ䜃x-z᩿㠃(h/L=5)

^Case1 _Case2

Case3 Case4

⣽ศ໬㡿ᇦ

⤖ᯝ(ԥpศᕸ)

Case1(0ӌzӌ0.1) Case4(0ӌzӌ2.0)

ึᮇ᱁Ꮚ

Case2(0ӌzӌ0.5) Case3(0ӌzӌ1.0)

` Case1

䠖ᅽຊኚື䛜ῶ⾶

` Case2

䠖᭱䜒኱䛝䛺ᅽຊኚື

` Case3,4䠖ศᕸ䛜Ᏻᐃ

ᑐ㇟㠃ཬ䜃x-z᩿㠃(h/L=5)

Case1 Case2

Case3 Case4

⣽ศ໬㡿ᇦ

(8)

` ⣽ศ໬㡿ᇦ(z㍈᪉ྥ)䛻䜘䜚Ἴᙧ䛜ኚ໬

z h/L=3䠖Case3(0ӌzӌ1.0)

䛷཰᮰

z Z=0.5䛾䛸䛝ึᮇᅽຊୖ᪼䛜᭱኱䛻

z h/L=5䠖ᮍ཰᮰

⤖ᯝ(ᅽຊἼᙧ)

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 15

-0.02 -0.01 0 0.01 0.02 0.03

-1.5 -1 -0.5 0 0.5 1

h/L=3.0

nona dp Ca se1(z0.1) Ca se2(z0.5) Ca se3(z1.0) Ca se4(z2.0)

4 3

¸ ¹

¨ ·

© ' §

L h p

p

4 1

¸ ¹

¨ ·

© ' §

L h L

x

-0.02 -0.01 0 0.01 0.02 0.03

-1.5 -1 -0.5 0 0.5 1

h/L=5.0

nona dp Ca se1(z0.1) Ca se2(z0.5) Ca se3(z1.0) Ca se4(z2.0) Exp

4 3

¸ ¹

¨ ·

© ' §

L h p

p

4 1

¸ ¹

¨ ·

© ' §

L h L

x

h/L=5.0 h/L=3.0

Ἴᙧྲྀᚓ఩⨨

⤖ᯝ(⣽ศ໬㡿ᇦ䛾ᅽຊศᕸ䜈䛾ᙳ㡪2)

x-z᩿㠃(h/L=3)䛷䛾ԥpศᕸ

Case2(0ӌzӌ0.5) Case3(0ӌzӌ1.0)

Case4(0ӌzӌ2.0)

` ᅽຊἼᙧ䜢ྲྀᚓ䛩䜛㝿䠈㡿ᇦ➃㒊䛾ᙳ㡪䜢⪃៖䛩䜛ᚲせᛶ

⣽ศ໬㡿ᇦ

(9)

ᚑ᮶䛾ᮏᡭἲ䛻䛚䛡䜛ၥ㢟Ⅼ

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 17

z タᐃ䛧䛯᭱ᑠ᱁Ꮚ䝃䜲䝈(ศ๭㝈ᗘ䠖5e-2) 䛷䛿Ἴᙧ䛜ῶ⾶

z Z㍈᪉ྥ(䝇䝟䞁᪉ྥ)䛾⣽ศ໬㡿ᇦ䛻䜘䜚,

ྲྀᚓ䛥䜜䜛ᅽຊἼᙧ䛜ኚ໬

¾

䜘䜚⣽䛛䛺⣽ศ໬(ศ๭㝈ᗘ䛾⦰ᑠ)

¾

⣽ศ໬㡿ᇦ䛾ᣑᙇ(㡿ᇦ䛾ᙳ㡪䛾᳨ド)

ڹ ᱁ᏊⅬ䛾ቑຍ䛻䜘䜚,ᚑ᮶䛾䜎䜎䛷䛿ィ⟬䝁䝇䝖䛜㠀⌧ᐇⓗ

z

⣽ศ໬㡿ᇦ䜢᭱ᑠ䝃䜲䝈䜎䛷⣽ศ໬䛩䜛䛯䜑,᱁ᏊⅬቑຍ䛜ⴭ䛧䛔

z

ศ๭㝈ᗘ䜢⾲㠃᱁Ꮚ䝃䜲䝈(1e-2௨ୗ)䛻䛩䜛䛸,䝰䝕䝹㏆ഐ䛾ᩘ್ㄗᕪ 䛾ᙳ㡪䜢ཷ䛡䜛

ุᐃ䛾ᨵၿ䛜ᚲせ

᱁ᏊⅬᩘቑຍ䛻┤⤖

ᅽຊ໙㓄䛻䜘䜛䝣䜱䝹䝍䝸䞁䜾

` ᚑ᮶

`

⠇Ⅼᇶ‽䛷䛾ุᐃ(ྛ⠇Ⅼ䛾ᅽຊ໙㓄䛾኱䛝䛥)

`

㜈್䜢ᡭື䛷ධຊ䠈ྛ⠇Ⅼ䛾್䛜㜈್䜢ୗᅇ䜛ሙྜ䛻㡿ᇦุ

ᐃ䛛䜙㝖እ

` ᪂䛧䛔ᣦᶆ

`

㎶ᇶ‽䛷䛾ุᐃ

` (ྛ㎶䛻᥋䛩䜛⠇Ⅼ䛾ᅽຊ໙㓄್䠈edge䛾㛗䛥)

`

ධຊ䛥䜜䛯≀⌮㔞䛛䜙㜈್䜢タᐃ

`

ᚲせ䛻ᛂ䛨䛶㔜䜏௜䛡䜢᳨ウ

edge L edge

p

f x ^|ѭp| ^edge

^{䛻2⠇Ⅼ䛾ᖹᆒ್}

|ѭp| _edge , L _edge

䛻㔜䜏௜䛡↓䛧

(10)

䝣䜱䝹䝍㜈್䛾タᐃ

0 50000 100000 150000 200000 250000 300000

1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 1.0E+00

ed g e ᩘ

**|ѭp|*Edge_length**

䝣䜱䝹䝍ᣦᶆศᕸ

䝣䜱䝹䝍ᣦᶆ䛾ศᕸ䛷᭱኱ᩘ䜢䜒䛴್䜢㜈್䛸䛧㜈್௨ୖ䛾㡿ᇦ䜢ุᐃ㡿ᇦ䛻タᐃ

|ѭp|

㎶䛾㛗䛥

3.3E-4 ⁰ ⁰

50000 50000 100000 100000 150000 150000 200000 200000 250000 250000 300000

⣽ศ໬ุᐃ

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 19

䝣䜱䝹䝍䛾ẚ㍑(PGF 1e-2 , edge)

ྛ⠇Ⅼ䛤䛸䠈E

_thr =1.e-2

ྛ㎶䛤䛸䠈(¶

thr = 3.3e-4

9᱁Ꮚ䛜⣽䛛䛔䜋䛹䝣䜱䝹䝍䛜ᙉ䛟ാ䛟

¾᱁Ꮚ䝃䜲䝈䛻ᛂ䛨䛯䝣䜱䝹䝍䝸䞁䜾

ᙉ

ᙅ 䝣䜱䝹䝍ᙉ䛥

(11)

᱁ᏊⅬᩘ: 130୓Ⅼ

PGF䠖 1.e-2(node)

ศ๭㝈ᗘ䠖

5e.-2

⣽ศ໬ᅇᩘ䠖18

᱁ᏊⅬᩘ䠖䠔䠒୓Ⅼ

PGF: edge

ศ๭㝈ᗘ䠖

5e.-2

⣽ศ໬ᅇᩘ䠖7

᱁ᏊⅬᩘ: 170୓Ⅼ

PGF: edge

ศ๭㝈ᗘ䠖

1e.-2

⣽ศ໬ᅇᩘ䠖10

᱁Ꮚẚ㍑

` 䝣䜱䝹䝍䛻㎶㛗䜢⪃៖䛩䜛䛣䛸䛷,ᅽຊ໙㓄䞉㎶㛗䛻ᛂ䛨䛯⣽ศ໬

䛜ྍ⬟䛻

䕿䜘䜚⣽䛛䛺⣽ศ໬䛜ྍ⬟

(䜘䜚⣽䛛䛺ศ๭㝈ᗘ)

䕧㐲᪉䛾໙㓄䛜ᑠ䛥䛔㒊ศ䛷,༑ศ䛺⣽ศ໬䛜㞴䛧䛔

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 21

h/L=1.0

`

⠇Ⅼᇶ‽䛾䝣䜱䝹䝍

䕿㐲᪉䛾⣽ศ໬䛻᭷ຠ

䕧ศ๭㝈ᗘ䜢⣽䛟䛷䛝䛺䛔

`

㎶ᇶ‽䛾䝣䜱䝹䝍

䕿ศ๭㝈ᗘ䜢䜘䜚⣽䛟䛷䛝䜛

䕿䝰䝕䝹㏆ഐ䛾ᩘ್ㄗᕪ䜢㝖ཤྍ⬟

䕧㐲᪉䛾⣽ศ໬䛷༑ศ䛺⣽ศ໬䛜ᚓ 䜙䜜䛺䛔

ᅽຊ໙㓄䛾ẚ㍑

-0.02 -0.01 0 0.01 0.02 0.03

-1 -0.5 0 0.5 1

h=3

PGF_1e-2 div5e-2 PGF_edge div5e-2 PGF_edge div1e-2

-0.02 -0.01 0 0.01 0.02 0.03

-1.5 -1 -0.5 0 0.5 1

h/L=1

PGF_e-2 div_5e-2 PGF_edge div_5e-2 PGF_edge div_1e-2

-0.02 -0.01 0 0.01 0.02 0.03

-1 -0.5 0 0.5 1

h/L=5

Exp

PGF_1e-2 div5e-2

PGF_edge div5e-2

PGF_edge div1e-2

(12)

䝣䜱䝹䝍㜈್䛾ኚ໬

2010/11/26 Yusuke OKI, Dept. of Aerospace Engineering, Tohoku Univ. JAPAN 23

`

⣽ศ໬䛻䜘䜛⤖ᯝ䛾ᨵၿ䛻䜘䜚,䝣䜱䝹䝍䛾㜈್䛜኱䛝䛟䛺䜛

(䝣䜱䝹䝍䛜ᙉ䛟䛺䜛᪉ྥ䜈䝅䝣䝖)

䕿䜘䜚⣽䛛䛺⣽ศ໬䛻᭷ຠ

䕧㐲᪉䛷䛿䝣䜱䝹䝍䛜ᙉ䛩䛞,⣽ศ໬䛜୙༑ศ䛻

ᣦᶆ䛾㔜䜏௜䛡,㜈್䛾Ỵᐃἲ䛾ᨵၿ

0 200000 400000 600000 800000 1000000 1200000

1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 1.0E+00

ed g e ᩘ

**|ѭp|*Edge_length**

䝣䜱䝹䝍ᣦᶆศᕸ

⣽ศ໬๓

⣽ศ໬ᚋ

3.3E-4 2.2E-3

⤖ゝ䞉௒ᚋ䛾ㄢ㢟

` ⤖ゝ

ż

ᩘ್ㄗᕪ㝖ཤ䛾䛯䜑䛻䠈ᅽຊ໙㓄䞉㎶㛗䜢ᣦᶆ䛸䛩䜛䝣䜱䝹䝍䜢ᑟධ䛧䠈ᣦ ᶆ䛾ศᕸᩘ䛛䜙䝣䜱䝹䝍㜈್䜢⮬ື䛷ồ䜑䜛䜘䛖ኚ᭦䜢ຍ䛘䛯

ż

䝣䜱䝹䝍䛻㎶㛗䜢⪃៖䛩䜛䛣䛸䛷ᅽຊ໙㓄䞉㎶㛗䛻ᛂ䛨䛯⣽ศ໬䛜⾜䜟䜜䠈 ᚑ᮶௨ୖ䛾⣽ศ໬䜢⾜䛖㝿䛾ィ⟬䝁䝇䝖䛾ῶᑡ䜢☜ㄆ䛧䛯

ż

୍᪉䛷䠈㜈್䛾⮬ື໬䛻䜘䜛䝣䜱䝹䝍ᙉᗘ䛾ኚ໬䛻䜘䜚䠈㐲᪉䛷䛾⣽ศ໬

䛜୙༑ศ䛸䛺䜛䛣䛸䜢☜ㄆ䛧䛯

`

௒ᚋ䛾ㄢ㢟

ż

䝣䜱䝹䝍䛾ᣦᶆཬ䜃㜈್Ỵᐃἲ䛾ᨵၿ

ż

䜘䜚⣽䛛䛺⣽ศ໬䜢⾜䛳䛯㝿䛾Ἴᙧ⢭ᗘ䛾᳨ド

ż

⣽ศ໬㡿ᇦ䛜ཬ䜌䛩Ἴᙧ䜈䛾ᙳ㡪䛾᳨ド

䝋䝙䝑䜽䝤䞊䝮᥎⟬䛾䛯䜑䛾㧗⢭ᗘ㏆ഐሙᅽ ຊἼᙧ᥎⟬ᢏ⾡䛻㛵䛩䜛◊✲䠄䛭䛾䠎䠅