物理学特殊講義I（MC向け集中） 流体力学編

I MC
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AMR HD/MHD
Matsumoto+/05
PDF
AMR/
19
0.6
20
log column density (cm-2)
21
22
t = 6.90213E+05 yr, step = 214000
tp = 1.76021E+04 yr
23
21.0
→
log column density (cm-2)
22.0
22.5
23.0
21.5
t = 6.90213E+05 yr, step = 214000
tp = 1.76021E+04 yr
(a)
0.4
Matsumoto+/15
24.0
23.5
(b)
0.10
z (pc)
z (pc)
0.2
0.0
0.05
-0.2
-0.4
-0.6
0.00
0.1 pc
-0.6
22.5
0.05 pc
-0.4log column
-0.2 density
0.0
0.2 -2) 0.4
(cm
x (pc)
23.0
23.5
24.0
1000 t = 6.90213E+05 yr, step = 214000
tp = 1.76021E+04 yr
offset = (-2.84E+04, 1.05E+04) AU
0.6
24.5
23.0
-0.20
23.5
-2
-0.15density (cm
-0.10
log column
)
x24.5
(pc)
24.0
25.0
25.5
t = 6.90213E+05 yr, step = 214000
tp = 1.76021E+04 yr
offset = (-2.84E+04, 1.05E+04) AU
(c)
-0.05
26.0
(d)
50
500
z (AU)
z (AU)
1
0
-500
0
-50
2
500 AU
-1000
-1000
-500
0
50 AU
0
x (AU)
500
1000
-50
0
x (AU)
50
6
AMR
log n (cm-3)t = 6.9674513E+05 yr
t = 6.9674513E+05 yr
0.6
log n (cm-3)
10
0.04
10
8
8
0.4
0.02
y (pc)
y (pc)
0.2
0.0
6
6
-0.2
0.00
-0.4
4
4
-0.6
-0.02
2
-0.6
-0.4
-0.2
0.0
x (pc)
0.2
0.4
0.6
2
-0.16
-0.14
x (pc)
-0.12
-0.10
7
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AMR
PC
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• PC
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AMR
My/KONAN
(CFD)
(MHD)
(11/28)
(11/25,26)
(11/27)
Numerical/Computation/of/Internal/and/
External/Flows,/Computational/Methods/for/
Inviscid and/Viscous/Flows/
(Wiley/Series/in/Numerical/Methods/in/
Engineering)/(
)/
use/pre/
formatted/date/that/complies/with/legal/
requirement/from/media/matrix/–
1990/4
Charles/Hirsch/(
)
4cm
Riemann/Solvers/and/Numerical/Methods/
for/Fluid/Dynamics:/A/Practical/Introduction/
(
)/
use/pre/formatted/date/
that/complies/with/legal/requirement/from/
media/matrix/– 2009/4/27
Eleuterio F./Toro/( )
HLL
Computational/Gasdynamics (
)/
use/pre/formatted/date/that/
complies/with/legal/requirement/from/
media/matrix/– 1998/6/13
Culbert B./Lan
use/pre/
formatted/date/that/complies/with/legal/
requirement/from/media/matrix/– 1994/4
( )
(
)/
use/pre/formatted/date/that/
complies/with/legal/requirement/from/
media/matrix/– 2007/8
(
),/
(
),/
(
)
2/(
2
=
)/
use/pre/formatted/date/that/
complies/with/legal/requirement/from/
media/matrix/– 1971/11
( ),/
( ),/
(
)
17
18
X
19
IC2087
Handbook/of/Star/Forming/regions
20
Taurus/filament/B211,/B213
DSS2
APEX
22
HP
23
H13CO+
T
NANTEN
HH46/47
ESO/
ALMA
25
(
pc)
(0.1
0.01/pc)
1AU →
(~100/AU)
T
(0.01AU)
(1AU)
(0.01/AU)
=%
27
vs/
https://www.youtube.com/watch?v=XRJx1ba_6DE
!⋅# ≠0
!⋅#= 0
•
•
•
•
•
(MHD)
2
∂2u
∂
u
2
−
c
=
0
∂t2
∂x2
∂u
∂2u
=k 2
∂t
∂x
∂2u ∂2u
+
=
ρ
∂x2
∂y 2
→
→
∂2u
∂2u
∂2u
A 2 +B
+ C 2 + ···
∂x
∂x∂y
∂y
⎧
⎪
⎨> 0 hyperbolic PDE
2
B − 4AC = = 0 parabolic PDE
⎪
⎩
< 0 elliptic PDE
2
∂2u
∂
u
2
−
c
=
0
∂t2
∂x2
∂u
∂2u
=k 2
∂t
∂x
∂2u ∂2u
+
=
ρ
∂x2
∂y 2
initial/value/problem
boundary/value/problem
Numerical/recipes
36
•
–
–
•
•
–
•
du/dx/=/0/
''+.
=0
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',
'( '+
+
=0
') ',
'( '+
+
= / Δ, 1 + /(Δ) 1 )
') ',
'( '+ '4 '6
+
+
+
=0
') ', '5 '7
MHD
/