=
p
i
T
i,j
b
+
L
ρc
p
J
i,j
−
1
−
b
−
R
ρc
p
J
i,j
+1
+
+
T
i,j
+1
b
−
R
ρc
p
J
i,j
+1
−
T
i,j
−
1
b
+
L
ρc
p
J
i,j
−
1
,
(64)
где
b
±
R
=
1
2
U
i,j
+1/2
±
U
i,j
+1/2
, b
±
L
=
1
2
U
i,j
−
1/2
±
U
i,j
−
1/2
,
(65)
U
i,j
±
1/2
=
1
2
(
U
i,j
+
U
i,j
±
1
)
.
(66)
Интегрирование в направлении
η
производится аналогично
.
В итоге
получается
5-
точечная конечно
-
разностная схема
A
i,j
T
n
+1
i
−
1
,j
+
B
i,j
T
n
+1
i
+1
,j
+ ˉ
A
i,j
T
n
+1
i,j
−
1
+ ˉ
B
i,j
T
n
+1
i,j
+1
−
C
i,j
T
n
+1
i,j
+
F
i,j
= 0
,
(67)
где
A
i,j
=
a
+
L
(
ρc
p
/
J
)
i
−
1
,j
p
i
+
a
−
h
p
−
i
p
i
, B
i,j
=
−
a
−
R
(
ρc
p
/
J
)
i
+1
,j
p
i
+
a
+
h
p
+
i
p
i
;
(68)
ˉ
A
i,j
=
b
+
L
(
ρc
p
/
J
)
i,j
−
1
q
j
+
b
−
h
q
−
j
q
j
,
ˉ
B
i,j
=
−
b
−
R
(
ρc
p
/
J
)
i,j
+1
q
j
+
b
+
h
q
+
j
q
j
;
(69)
C
i,j
=
A
i,j
+
B
i,j
+ ˉ
A
i,j
ˉ
B
i,j
ρc
p
J
i,j
1
τ
;
(70)
a
±
R
=
1
2
V
i
+1/2
,j
±
V
i
+1/2
,j
, a
±
L
=
1
2
V
i
−
1/2
,j
±
V
i
−
1/2
,j
;
(71)
V
i,j
±
1/2
=
1
2
(
V
i,j
+
V
i
±
1
,j
) ;
(72)
F
i,j
=
c
p i,j
ρ
i,j
T
n
i,j
J
i,j
τ
+
Q
dis,i,j
+
Q
p,i,j
+
Q
α,i,j
+
Q
xy,i,j
+
Q
rad,i,j
;
(73)
Q
dis,i,j
=
μ
i,j
J
i,j
Re
5
X
k
=1
Q
(
k
)
dis,i,j
;
(74)
Q
(1)
dis,i,j
= 2
ξ
x,i,j
+1
u
i,j
+1
J
i,j
+1
−
ξ
x,i,j
−
1
u
i,j
−
1
J
i,j
−
1
1
2
q
j
+
+
η
x,i
+1
,j
u
i
+1
,j
J
i
+1
,j
−
η
x,i
−
1
,j
u
i
−
1
,j
J
i
−
1
,j
1
2
p
i
2
;
(75)
ISSN 0236-3941.
Вестник МГТУ им
.
Н
.
Э
.
Баумана
.
Сер
. “
Машиностроение
”. 2005.
№
3 19
