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Modification of the LS-STAG Immersed Boundary Method for Simulating Turbulent Flows
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5
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In 2D case, the cut-cells can be classified into trapezoidal, triangular and
pentagonal cells. Examples of each type cut-cells are shown on Fig. 4.
To preserve the five-point structure of the stencil of the MAC method, which can
be considered as some kind of ''predecessor'' of the LS-STAG method, we need
to make distinction between the discretization of the normal and shear stresses [2]
(Fig. 4). It is conveniently to sample the eddy viscosity
,
t
the turbulent kinetic
energy
,
k
the dissipation rate of the kinetic energy,
and the specific dissipation rate
of kinetic energy
at the same points as the shear stresses. Thus, in case of the
LS-STAG method usage for RANS-based models the fourth mesh (
xy
-mesh) with cells
1
,
1
=( ,
) ( ,
)
xy
c c
c c
i
i
i j
j
j
x x
y y
is needed. The faces of these cells are
,
xy
i j
(Fig. 2) and their
areas are
,
.
xy
i j
M
If
i
and
j
take values from ranges
1,...,
N
and
1,..., ,
M
respectively,
the base mesh contains
=
E NM
cells,
x
-mesh contains
=( 1)
x
E N M
cells,
y
-mesh
contains
= ( 1)
y
E N M
cells and
xy
-mesh contains
=( 1)( 1)
xy
E N M
cells.
It is possible to assign a weight
,
i j
to each cell
,
i j
of the base mesh:
,
,
,
0,
if
is the solid cell;
= 1/ 3, if
is the triangular cell;
1/ 4, otherwise.
i j
i j
i j
Fig. 4.
Location of the variables discretization points in case of base types cells of the LS-STAG
mesh:
a —
Cartesian Fluid Cell;
b —
North Trapezoidal Cell;
c —
Northwest Pentagonal Cell;
d —
Northwest
Triangle Cell