2. $B6u4VJ}8~$NN%;62=(B

$B$3$N@a$G$O6u4VHyJ,$NN%;62=$NJ}K!$H$=$N$?$a$KI,MW$H$J$kJ?6QA`:n(B, $B6-3&>r(B $B7o$NM?$(J}$K$D$$$F@bL@$9$k(B. $BN%;62=$O(B 2 $B Fig.1.1 $B$N6u4V$N0LCV$rI=$9E:;z$H$7$F(B, $x$ $BJ}8~%U%i%C%/%9$N3J;RE@$r(B ($i(u),k$), $z$ $BJ}8~%U%i%C%/%9$N3J;RE@$r(B ($i,k(w)$), $B%9%+%i!), $B3J;R$N3Q$KEv$?$kE@$r(B ($i(u), k(w)$) $B$H$9$k(B (Fig.1.1 $B;2>H(B). $BC"$7(B $1 \leq i(u) \leq im$, $1 \leq i \leq im$, $1 \leq k(w) \leq km$, $1 \leq k \leq km$ $B$G$"$k(B.

2.1 $BJ?6QA`:n(B

$B6u4VHyJ,$NN%;62=$r9T$&A0$K(B, $B$=$N$?$a$KI,MW$H$J$kJ?6QA`:n$rDj5A$7$F$*$/(B. $BNc$($P(B $x$ $BJ}8~%U%i%C%/%93J;RE@$GI>2A$5$l$kJQ?t$r%9%+%i!(B $B2A$9$k>l9g$O(B, $B%U%i%C%/%93J;RE@$NCM$rJ?6Q$7$F%9%+%i!<3J;RE@$G$NCM$H$_$J$9(B.

$BI,MW$H$J$kJ?6QA`:n$r0J2<$K<($9(B. $B$3$3$G$O(B $x$ $BJ}8~$N%U%i%C%/%93J;RE@$NJQ(B $B?t$r(B $u_{i(u), k}$, $z$ $BJ}8~$N%U%i%C%/%93J;RE@$NJQ?t$r(B $w_{i, k(w)}$, $B%9(B $B%+%i!<3J;RE@$NJQ?t$r(B $\pi_{i, k}$ $B$H$7$F$$$k(B.

$$\pi_{i(u),k} \equiv \frac{\pi_{i+1, k} + \pi_{i, k}}{2}$$ (2.1)

$$\pi_{i,k(w)} \equiv \frac{\pi_{i, k+1} + \pi_{i, k}}{2}$$ (2.2)

$$\pi_{i(u),k(w)} \equiv \frac{\pi_{i, k} + \pi_{i+1, k}+ \pi_{i, k+1}+ \pi_{i+1, k+1}}{4}$$ (2.3)

$$u_{i,k} \equiv \frac{u_{i(u), k} + u_{i-1(u), k}}{2}$$ (2.4)

$$u_{i,k(w)} \equiv \frac{u_{i(u), k+1} + u_{i-1(u), k+1} + u_{i(u), k} + u_{i-1(u), k}}{4}$$ (2.5)

$$u_{i(u),k(w)} \equiv \frac{u_{i(u), k+1} + u_{i(u), k}}{2}$$ (2.6)

$$w_{i,k} \equiv \frac{w_{i, k(w)} + w_{i, k-1(w)}}{2}$$ (2.7)

$$w_{i(u),k} \equiv \frac{w_{i+1, k(w)} + w_{i, k(w)} + w_{i+1, k-1(w)} + w_{i, k-1(w)}}{4}$$ (2.8)

$$w_{i(u),k(w)} \equiv \frac{w_{i+1, k(w)} + w_{i, k(w)}}{2}$$ (2.9)

2.2 $B6u4VHyJ,$NN%;62=(B

2.2.1 2 $B

$B6u4VHyJ,$r(B 2 $B $BJ}8~$N%U%i%C%/%93J;RE@$NJQ?t$r(B $u_{i(u), k}$, $z$ $BJ}8~$N%U%i%C%/%93J;RE@$NJQ?t$r(B $w_{i, k(w)}$, $B%9%+%i!<3J;RE@$NJQ?t$r(B $\pi_{i, k}$ $B$H$7$F$$$k(B. $x$, $z$ $BJ}8~$H$b$K%U%i%C%/%93J;RE@$NJQ?t$r(B $\phi_{i(u), k(w)}$ $B$H$7$F$$$k(B.

$B$=$l$>$l$NJQ?t$KBP$7$FHyJ,$rI>2A$9$k3J;RE@$O0l0U$K7h$^$k(B. $B$=$N$?$a(B, $BB>$N3J;RE@$K$*$$$FHyJ,$rI>2A$9$k>l9g$K$OJ?6QA`:n$rMQ$$$k(B.

$$\left[\DP{\pi}{x} \right]_{i(u),k} \equiv \frac{\pi_{i+1, k} - \pi_{i, k}}{\Delta x}$$ (2.10)

$$\left[\DP{\pi}{z} \right]_{i,k(w)} \equiv \frac{\pi_{i, k+1} - \pi_{i, k}}{\Delta z}$$ (2.11)

$$\left[\DP{u}{x} \right]_{i,k} \equiv \frac{u_{i(u), k} - u_{i-1(u), k}}{\Delta x}$$ (2.12)

$$\left[\DP{u}{z} \right]_{i(u),k(w)} \equiv \frac{u_{i(u), k+1} - u_{i(u), k}}{\Delta z}$$ (2.13)

$$\left[\DP{w}{x} \right]_{i(u),k(w)} \equiv \frac{w_{i+1, k(w)} - w_{i, k(w)}}{\Delta x}$$ (2.14)

$$\left[\DP{w}{z} \right]_{i,k} \equiv \frac{w_{i, k(w)} - w_{i, k-1(w)}}{\Delta z}$$ (2.15)

$$\left[\DP{\phi}{x} \right]_{i,k(w)} \equiv \frac{\phi_{i(u), k(w)} - \phi_{i-1(u), k(w)}}{\Delta x}$$ (2.16)

$$\left[\DP{\phi}{z} \right]_{i(u),k} \equiv \frac{\phi_{i(u), k(w)} - \phi_{i(u), k-1(w)}}{\Delta z}$$ (2.17)

2.2.2 4 $B

2 $Bl9g$HF1MM$K(B, $B6u4VHyJ,$r(B 4 $B

$$\left[\DP{\pi}{x} \right]_{i(u),k} \equiv \frac{9}{8}\left(\frac{... ...\right) - \frac{1}{24}\left(\frac{\pi_{i+2, k} - \pi_{i-1, k}}{\Delta x}\right)$$ (2.18)

$$\left[\DP{\pi}{z} \right]_{i,k(w)} \equiv \frac{9}{8}\left(\frac{... ...\right) - \frac{1}{24}\left(\frac{\pi_{i, k+2} - \pi_{i, k-1}}{\Delta x}\right)$$ (2.19)

$$\left[\DP{u}{x} \right]_{i,k} \equiv \frac{9}{8}\left(\frac{u_{i(... ...ight) - \frac{1}{24}\left(\frac{u_{i(u)+1, k} - u_{i-2(u), k}}{\Delta x}\right)$$ (2.20)

$$\left[\DP{u}{z} \right]_{i(u),k(w)} \equiv \frac{9}{8}\left(\frac... ...ight) - \frac{1}{24}\left(\frac{u_{i(u), k+2} - u_{i(u), k-1}}{\Delta x}\right)$$ (2.21)

$$\left[\DP{w}{x} \right]_{i(u),k(w)} \equiv \frac{9}{8}\left(\frac... ...ight) - \frac{1}{24}\left(\frac{w_{i+2, k(w)} - w_{i-1, k(w)}}{\Delta x}\right)$$ (2.22)

$$\left[\DP{w}{z} \right]_{i,k} \equiv \frac{9}{8}\left(\frac{w_{i,... ...ight) - \frac{1}{24}\left(\frac{w_{i, k+1(w)} - w_{i, k-2(w)}}{\Delta z}\right)$$ (2.23)

$$\left[\DP{\phi}{x} \right]_{i,k(w)} \equiv \frac{9}{8} \left(\fra... ...{1}{24} \left(\frac{\phi_{i+1(u), k(w)} - \phi_{i-2(u), k(w)}}{\Delta x}\right)$$ (2.24)

$$\left[\DP{\phi}{z} \right]_{i(u),k} \equiv \frac{9}{8}\left( \fra... ...{1}{24}\left( \frac{\phi_{i(u), k+1(w)} - \phi_{i(u), k-2(w)}}{\Delta z}\right)$$ (2.25)

2.3 $B6u4VN%;62=$7$?4pACJ}Dx<0(B

2.3.1 $B@E?e05$N<0(B

$$\left[\DP{\overline{\pi}}{z}\right]_{i,k} = - \frac{g}{{c_{p}}_{d} [\overline{\theta_{v}}]_{i,k}}$$ (2.26)

$B4pK\>l$NL)EY(B $\overline{\rho}_{i,k}$ $B$O0J2<$N$h$&$K7W;;$9$k(B.

$$\overline{\rho}_{i,k} = \frac{p_{0}}{R_{d}} \frac{[\overline{\pi}^{c_{v}/R_{d}}]_{i,k}} {[\overline{\theta_{v}}]_{i,k}}$$ (2.27)

2.3.2 $B1?F0J}Dx<0(B

$$\DP{u_{i(u),k}}{t} = - u_{i(u),k}\left[\DP{u}{x}\right]_{i(u),k} - w_{i(u),k}\left[\DP{u}{z}\right]_{i(u),k}$$

$$- {c_{p}}_{d} [\overline{\theta_{v}}]_{i(u),k} \left[\DP{\pi}{x}\right]_{i(u),k} + \left[{\rm Turb}.{u}\right]_{i(u),k}$$ (2.28)

$$\DP{w_{i,k(w)}}{t} = - u_{i,k(w)}\left[\DP{u}{x}\right]_{i,k(w)} - w_{i,k(w)}\left[\DP{u}{z}\right]_{i,k(w)}$$

$$- {c_{p}}_{d} [\overline{\theta_{v}}]_{i,k(w)}\left[\DP{\pi}{z}\right]_{i,k(w)} + \left[{\rm Turb}.{w}\right]_{i,k(w)}$$

$$+ g \frac{\theta_{i,k(w)}}{\overline{\theta}_{i,k(w)}}$$

$$+ g \frac{\sum [q_{v}]_{i,k(w)}/M_{v}}{1/M_{d} + \sum [\bar{q_{v}}]_{i,k(w)}/M_{v}}$$

$$- g \frac{\sum [q_{v}]_{i,k(w)} + \sum [q_{c}]_{i,k(w)} + \sum [q_{r}]_{i,k(w)}} {1 + \sum [\bar{q_{v}}]_{i,k(w)}}$$ (2.29)

2.3.3 $B05NOJ}Dx<0(B

$$\DP{\pi_{i,k}}{t} + \frac{\overline{c}_{i,k}^{2}}{{c_{p}}_{d} \ov... ...{v}} u}{x} + \DP{\overline{\rho} \overline{\theta_{v}} u}{z} \right]_{i,k} = 0.$$ (2.30)

$B4pK\>l$N2;B.(B $\overline{c}$ $B$O0J2<$N$h$&$K7W;;$9$k(B.

$$\overline{c}_{i,k}^{2} = \frac{{c_{p}}_{d} R_{d}}{c_{v}} \overline{\pi}_{i,k} [\overline{\theta_{v}}]_{i,k}.$$ (2.31)

2.3.4 $BG.NO3X$N<0(B

$$\DP{\theta_{i,k}}{t} = - u_{i,k}\left[\DP{\theta}{x}\right]_{i,k} - w_{i,k}\left[\DP{\th... ...Turb}.{\theta}\right]_{i,k} + \left[{\rm Turb}.{\overline{\theta}}\right]_{i,k}$$

$$+ \Dinv{\overline{\pi}_{i,k}} \left([Q_{cnd}]_{i,k} + [Q_{rad}]_{i,k} + [Q_{dis}]_{i,k}\right)$$ (2.32)

2.3.5 mail protected],$N:.9gHf$NJ]B8<0(B

$$\DP{[q_{v}]_{i,k}}{t} = - u_{i,k} \left[\DP{q_{v}}{x} \right]_{i,k} - w_{i,k} \left[\DP{q_{v}}{x} \right]_{i,k} - w_{i,k} \left[\DP{\bar{q_{v}}}{x} \right]_{i,k}$$

$$+ [{\rm Src}.q_{v}]_{i,k} + [{\rm Turb}.{\overline{q_{v}}}]_{i,k} + [{\rm Turb}.{q_{v}}]_{i,k},$$ (2.33)

$$\DP{[q_{c}]_{i,k}}{t} = - u_{i,k} \left[ \DP{q_{c}}{x} \right]_{i,k} - w_{i,k} \left[ \DP{q_{c}}{x} \right]_{i,k} + [{\rm Src}.q_{c}]_{i,k} + [{\rm Turb}.{q_{c}}]_{i,k},$$ (2.34)

$$\DP{[q_{r}]_{i,k}}{t} = - u_{i,k} \left[ \DP{q_{r}}{x} \right]_{i,k} - w_{i,k} \left[ \DP{q_{r}}{x} \right]_{i,k} + [{\rm Src}.q_{r}]_{i,k}$$

$$+ [{\rm Fall}.q_{r}]_{i,k} + [{\rm Turb}.{q_{r}}]_{i,k}$$ (2.35)

2.4 $B6-3&>r7o(B

$B$3$3$G$ON%;62=$7$?JQ?t$KBP$9$k6-3&>r7o$NM?$(J}$r$^$H$a$k(B. $B9MN8$9$k6-3&>r(B $B7o$O(B, $B<~4|6-3&>r7o(B, $B6-3&$G$9$Y$j$J$7>r7o$H1~NO$J$7>r7o$G$"$k(B.

2.4.1 $B<~4|6-3&>r7o$NM?$(J}(B

$BNc$H$7$F(B, $x$ $BJ}8~%U%i%C%/%93J;RE@$KG[CV$5$l$?JQ?t(B $u_{i(u), k}$ $B$r9M$($k(B. $B7W;;NN0hFb$N(B $x$ $BJ}8~$NE:;z$r(B $1(u)\sim im(u)$ $B$H$7(B, $B8RBeItJ,$N3J;RE@?t(B $B$r(B $2$ $B$H$9$k(B(Fig.1.2$B;2>H(B). $B$3$N$H$-<~4|6-3&>r7o$O0J2<$N$h$&$KM?(B $B$($i$l$k(B.

$$u_{0(u), k} = u_{im(u), k}$$ (2.36)

$$u_{-1(u), k} = u_{im-1(u), k}$$ (2.37)

$$u_{im+1(u), k} = u_{1(u), k}$$ (2.38)

$$u_{im+2(u), k} = u_{2(u), k}$$ (2.39)

$B$?$@$7(B $k$ $B$OG$0U$N@0?t$G$"$j(B, $B$=$NHO0O$O(B $-1 \leq k \leq km + 2$ $B$G$"$k(B.

$z$ $BJ}8~%U%i%C%/%93J;RE@$KG[CV$5$l$?JQ?t(B, $B%9%+%i!<3J;RE@$KG[CV$5$l$?JQ?t(B $B$KBP$7$F$bF1MM$KM?$($k$3$H$,$G$-$k(B.

2.4.2 $B$9$Y$j$J$7>r7o$NM?$(J}(B

$B6-3&$GB.EY$r(B 0 $B$H$9$k(B. $B$3$N>l9g(B, $B6-3&$r$O$5$s$GJQ?t$NCM$,H?BP>N$K$J$k$h(B $B$&$KM?$($k(B.

$BNc$H$7$F(B $x$ $BJ}8~$K6-3&$rM?$($?>l9g$r9M$($k(B. $x$ $BJ}8~%U%i%C%/%93J;RE@$K(B $BG[CV$5$l$?JQ?t$KBP$7$F$O(B.

$$u_{0(u),k} = u_{im(u),k} = 0$$ (2.40)

$$u_{-1(u),k} = - u_{1(u),k}$$ (2.41)

$$u_{im+1(u),k} = - u_{im-1(u),k}$$ (2.42)

$$u_{im+2(u),k} = - u_{im-2(u),k}$$ (2.43)

$B$H$9$k(B. $B6-3&>e$KG[CV$5$l$F$$$J$$JQ?t$KBP$7$F$O(B,

$$\pi_{0,k} = - \pi_{1,k}$$ (2.44)

$$\pi_{-1,k} = - \pi_{1,k}$$ (2.45)

$$\pi_{im+1,k} = - \pi_{im,k}$$ (2.46)

$$\pi_{im+2,k} = - \pi_{im-1,k}$$ (2.47)

$B$H$9$k(B.

2.4.3 $B1~NO$J$7>r7o$NM?$(J}(B

$B6-3&>e$GK!@~J}8~B.EY$r(B 0, $B@\@~J}8~B.EY$NK!@~J}8~HyJ,$r(B 0 $B$H$9$k(B. $B$3$N>l(B $B9g(B, $B6-3&>e$GG[[email protected],$O6-3&$r$O$5$s$GJQ?t$NCM$,H?BP>N$K$J$k$h$&(B $B$KM?$((B, $B6-3&>e$KG[CV$5$l$F$$$J$$JQ?t$KBP$7$F$OJI$r$O$5$s$GJQ?t$NCM$,BP>N(B $B$K$J$k$h$&$KM?$($k(B.

$BNc$H$7$F(B $x$ $BJ}8~$K6-3&$rM?$($?>l9g$r9M$($k(B. $x$ $BJ}8~%U%i%C%/%93J;RE@$K(B $BG[CV$5$l$?JQ?t$KBP$7$F$O(B.

$$u_{0(u),k} = u_{im(u),k} = 0$$ (2.48)

$$u_{-1(u),k} = - u_{1(u),k}$$ (2.49)

$$u_{im+1(u),k} = - u_{im-1(u),k}$$ (2.50)

$$u_{im+2(u),k} = - u_{im-2(u),k}$$ (2.51)

$B$H$9$k(B. $B6-3&>e$KG[CV$5$l$F$$$J$$JQ?t$KBP$7$F$O(B,

$$\pi_{0,k} = \pi_{1,k}$$ (2.52)

$$\pi_{-1,k} = \pi_{1,k}$$ (2.53)

$$\pi_{im+1,k} = \pi_{im,k}$$ (2.54)

$$\pi_{im+2,k} = \pi_{im-1,k}$$ (2.55)

$B$H$9$k(B.