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p = \rho R T.
\end{displaymath}" |
(103) |
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p = \rho R^d T_v.
\end{displaymath}" |
(104) |
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\DP{\rho}{t}
+ \DP{}{x_j}( \rho v_j )
= 0.
\end{displaymath}" |
(105) |
$B$"$k$$$O(B, $B%i%0%i%s%8%e7A<0$G5-=R$9$l$P(B,
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\DD{\rho}{t}
+ \rho \Ddiv \Dvect{v}
= 0.
\end{displaymath}" |
(106) |
$B?e>x5$L)EY(B
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\DP{\rho^v}{t}
+ \DP{}{x_j} ( \rho^v v_j )
= S.
\end{displaymath}" |
(107) |
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\DD{q}{t} = S_q.
\end{displaymath}" |
(108) |
$B1?F0NLJ]B8B'$O(B, $B?e>x5$$N@8@.>CLG$K$H$b$J$&1?F0NLJQ2=$rL5;k$9$l$P
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\DP{}{t}(\rho v_i)
+ \DP{}{x_j}( \rho v_i v_j )
+ \DP{p}{x_i}
- \DP{\sigma_{ij}}{x_j}
+ \rho \DP{\Phi^*}{x_i}
= F'_i.
\end{displaymath}" |
(109) |
$B$3$3$G(B,
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 |
(110) |
$B$H$J$k(B. $B$3$3$G(B, $BG4@-9`$H30NO9`$r(B
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\rho \DD{\Dvect{v}}{t}
+ \Dgrad p
+ \rho \Dgrad \Phi^*
= \Dvect{F}.
\end{displaymath}" |
(111) |
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![\begin{displaymath}
\DP{}{t}
\left[ \rho
\left( \frac{1}{2} \Dvect{v}^2
+...
...v_j
+ p v_j - \sigma_{ij}v_i
\right]
= \rho Q + F'_i v_i,
\end{displaymath}](img355.png) |
(112) |
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\DP{}{t} \left( \frac{1}{2} \rho v_i^2 + \rho \Phi^* \right...
...ht)
= p \DP{v_j}{x_j} - \sigma_{ij} \DP{v_i}{x_j} + F'_i v_i,
\end{displaymath}" |
(113) |
$B$H$J$k(B. $B<0(B (A.14) $B$+$i<0(B (
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\DP{}{t} ( \rho \varepsilon )
+ \DP{}{x_j} ( \rho \varepsi...
... )
= - p \DP{v_j}{x_j} + \sigma_{ij} \DP{v_i}{x_j}
+ \rho Q.
\end{displaymath}" |
(114) |
$BO"B3$N<0$rMQ$$$F%i%0%i%s%8%e7A<0$K=q$-D>$;$P(B
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\rho \DD{\varepsilon}{t}
= \frac{p}{\rho} \left( \DD{\rho}{t} \right)
+ \rho Q.
\end{displaymath}" |
(115) |
$B$3$3$G(B, $B303&$+$i$N2CG.$N9`$HG4@-$K$h$k2CG.$N9`$r$^$H$a$F(B
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\DD{c_p T}{t} = \frac{1}{\rho} \DD{p}{t} + Q^*,
\end{displaymath}" |
(116) |
$B$H$J$k(B. $B$3$3$G(B,
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\DD{T}{t} = \frac{1}{c_p^d \rho} \DD{p}{t} + \frac{Q^*}{c_p^d}.
\end{displaymath}" |
(117) |
11
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\left( \DD{\psi}{t} \right)_{\rm a}
= \left( \DD{\psi}{t} \right)_{\rm r},
\end{displaymath}" |
(118) |
$B$,@.$j$?$D(B.
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 |
(119) |
($B>ZL@(B) $BG$0U$N%Y%/%H%k(B
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|
 |
 |
(120) |
$B$HI=$7(B, $B2sE>7O$G$O(B
|
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 |
(121) |
$B$HI=$9(B.
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 |
(123) |
$B$5$i$K(B, $B<0(B(A.21) $B$G(B
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 |
(124) |
$B$HJQ49$G$-$k(B.
$BJQ49$N<0(B (A.26) $B$rMQ$$$F1?F0J}Dx<0$r2sE>7O$G5-=R$9$k(B.
 |
(125) |
$B$3$3$G(B, $B=ENO2CB.EY(B
$B$rDj5A$9$l$P(B, $B1?F0J}Dx<0$O(B
 |
(126) |
$B$H$J$k(B.
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13
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 |
(127) |
![\begin{displaymath}
\Ddiv \Dvect{A}
= \frac{1}{h_1 h_2 h_3}
\left[ \DP{}{\x...
...\xi_2} ( h_1 h_3 A_2)
+ \DP{}{\xi_3} ( h_1 h_2 A_3)
\right],
\end{displaymath}](img410.png) |
(128) |
![\begin{displaymath}
\nabla^2 \bullet
= \frac{1}{h_1 h_2 h_3}
\left[ \DP{}{\...
...eft( \frac{h_1 h_2}{h_3} \DP{\bullet}{\xi_3} \right)
\right],
\end{displaymath}](img411.png) |
(129) |
![\begin{displaymath}
\Drot \Dvect{A}
= \left( \frac{1}{h_2 h_3}
\left[ \DP{(h_...
...DP{(h_2 A_2)}{\xi_1} - \DP{(h_1 A_1)}{\xi_2} \right]
\right),
\end{displaymath}](img412.png) |
(130) |
 |
(131) |
![\begin{displaymath}
\DD{\Dvect{v}}{t}
= \sum^3_{k=1} \Dvect{e}_k
\left[ \DP{v...
...{v_k}{h_k} \frac{1}{h_j} \DP{h_k}{\xi_j} \right) v_j
\right].
\end{displaymath}](img414.png) |
(132) |
$B=ENO2CB.EY(B
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h_\lambda = r \cos \varphi, \ \ h_\varphi = r, \ \ h_r = 1.
\end{displaymath}" |
(136) |
$B$7$?$,$C$F(B, $B%9%+%i!<(B
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$B$K4X$9$kHyJ,I=8=$O
 |
(137) |
![\begin{displaymath}
\Ddiv \Dvect{A}
= \frac{1}{r^2 \cos \varphi}
\left[ r \...
...hi A_{\varphi})
+ \cos \varphi \DP{}{r} ( r^2 A_r )
\right],
\end{displaymath}](img430.png) |
(138) |
![\begin{displaymath}
\nabla^2 \bullet
= \frac{1}{r^2 \cos \varphi}
\left[ \D...
...}{r} \left( r^2 \cos \varphi \DP{\bullet}{r} \right)
\right],
\end{displaymath}](img431.png) |
(139) |
 |
(141) |
$B<+E>3QB.EY%Y%/%H%k$NI=8=$O
$B$7$?$,$C$F(B, $B1?F0J}Dx<0$O(B
$BO"B3$N<0$O(B
 |
(148) |
$BG.NO3X$N<0$O(B
 |
(149) |
$B>uBVJ}Dx<0$O(B
 |
(150) |
$B?e>x5$$N<0$O(B
 |
(151) |
$B$3$3$G(B,
 |
(152) |
$B$G$"$k(B.
13
1313
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1313
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 |
(153) |
$B$3$N$H$-(B, $B1?F0%(%M%k%.!<$NJ]B8B'$r9MN8$7$F(B, $B?eJ?J}8~$N1?F0J}Dx<0$KBP$7(B
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14$B$7$?$,$C$F(B, $B@ENO3XJ?9U6a;w$N:]$K1tD>@.J,$N<0$+$iMn$H$7$?9`(B(2),(4),(5)
[email protected],$N<0$N9`$b
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$B$K$h$kHyJ,$O$9$Y$F3$H49bEY(B
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 |
(157) |
 |
(158) |
 |
(159) |
 |
(160) |
 |
(161) |
 |
(162) |
 |
(163) |
$B$3$3$G(B,
 |
(164) |
 |
(165) |
derivation/derivation-sigmacoord
14
1414
14
1414
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 |
(166) |
$BH/;6(B:
 |
(167) |
$B1?F0J}Dx<0$N(B
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16
 |
(176) |
$B12EYJ}Dx<0(B
$BH/;6J}Dx<0(B
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 |
(184) |
$B@E?e05$N<0(B
 |
(185) |
$B1?F0J}Dx<0(B17
 |
(186) |
 |
(187) |
$B$3$3$G(B,
$BG.NO3X$N<0(B
$B?e>x5$$N<0(B
 |
(191) |
$B<0(B(A.17) $B$GF3F~$7$?(B
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Yasuhiro MORIKAWA
$BJ?@.(B19$BG/(B6$B7n(B8$BF|(B