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I.K. Marchevsky, V.V. Puzikova
26
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5
Then
,
xy
i j
M
can be expressed through the area of base mesh cells:
, 1 , 1
1,
1,
,
,
, 1 , 1
,
=
.
xy
i j
i j
i
j i
j
i j i j
i j
i j
i j
M V
V
V
V
Here
,
i j
V
is the area of the cell
,
.
i j
Since
t
and shear Reynolds or subgrid stresses (5) are sampled at the same
points, it follows that
,
,
,
,
| =
,
t
t
xy i j
i j
i j
i j
u v
y
x
(8)
whereas averaged values of turbulent viscosity
,
t
i j
and the turbulent kinetic energy
,
i j
k
should be used for the computation of the normal Reynolds or subgrid stresses
(4):
,
,
,
,
,
,
,
,
2
2
| = 2
;
| = 2
;
3
3
t
t
t
t
i j
xx i j
yy i j
i j
i j
i j
i j
i j
u
v
k
k
x
y
,
,
,
,
, 1
1,
1, 1
,
,
, 1
1,
1, 1
= (
);
= (
).
t
t
t
t
t
i j
i j
i j
i j
i j
i
j
i
j
i j
i j
i j
i
j
i
j
k
k k k
k
(9)
Formulae for normal stresses
,
i j
u
x
and
,
i j
v
y
computation are the following:
,
1,
,
1,
1,
,
,
,
,
(
)
;
/
u
u
u
u ib
i j
i
j
i j
i
j
i
j
i j
i j
i j
j
i j
u
u
u
u
x
V y
,
, 1
,
, 1
, 1 ,
,
,
,
(
)
.
/
v
v
v
v ib
i j
i j
i j
i j
i j
i j i j
i j
i
i j
v
v
v
v
y
V x
formulae for shear stresses
,
i j
u
y
and
,
i j
v
x
computation depend on the type of
,
xy
i j
cell:
, 1 ,
,
, 1
1
, 1
,
,
, 1
, 1
,
, 1
1
, 1
,
,
,
,
,
,
, 1
,
,
,
if
0,
0;
(
) / 2
( ,
)
=
, if
= 0,
0;
/ 2
( ,
)
=
,
if
0,
= 0;
/ 2
i j
i j
u
u
i j
i j
u
u
j
j
i j
i j
ib s
ib
i j
i
i j
u
u
i j
i j
u
j
i j
i j
i j
ib n
ib
i
i j
i j
u
u
i j
i j
u
j
i j
i j
u u
y
y
u u x y
u
u
y
y
y
u x y u
u
y
y