Page 381 - Computational Fluid Dynamics for Engineers

372 12. Compressible Navier-Stokes Equations

On the left boundary subdomains i?ij, close to inflow and wall bound-
ary, i = 1

E E F F
1 + 1/2J ~ 1-1/2J l,j+l/2 ~ l , i - l / 2
dt Ax Ay
E
E
JL_ ( v)l+l/2j ~~ ( v)l-l/2,j ( ^ ) l , j + l / 2 ~ ( - ^ ) l j - l / 2
+ +
Re Ax Ay
t
Note hat l - l / 2 = > 0
_ / ^ i + i ^ + g i , i . ^
d Q l j
J i j + i ~ ^ i j - i
^ zAx 2zAy
1 ( ^ ) l + l / 2 J ~ ( ^ ) o , j ( ^ ) l j + l/2 ~ ( ^ ) l J - l / 2
+ Re Ax Ay

u
> x)l-l/2j
Ax/2 Ax
^l+l/2,j+l/2 ~ ^ l - l / 2 j + l/2
u
\ x)lj+l/2
Ax
U
_ (^1 + 1J+1 + ^1 + 1J + 1J+1 + ^ l j ) / 4 ~ (^OJ+l + u 0,j)/ 2

, v _ ^ l + l / 2 J - l / 2 ~ ^ l - l / 2 , j - l / 2

_ (^i+i,j + ^ i + i j - i + ^i,j + ^ i j - i ) / 4 ~ (UQJ + ^ Q j - i ) / 2

On the right boundary subdomains fZij, close o right outflow bound-
t
ary, i = I

E
F
9Qi, E I+1/2J ~ I-1/2J \ ( l J + l / 2 ~ F Ij~l/2
1 —
dt
F
F
E
E
1 ( v)l+l/2,j ~ ( v)l-l/2j ( v)l,j+l/2 ~ ( v)lJ-l/2
+
R^ Ax Ay
Note that 1 + 1/2 => J + 1
Eij+Ej-ij
Fi,j+x - J / j - i
dt Ax 2Ay
F
1 (•SuXf+lj - {Ev)I-l/2,j , ( - ^ ) J J + l / 2 ~~ (• «)7,3-l/2
+
Re Ax Ay