SIMPLE Method on Non-staggered Grids - Department of ...

where
a = ( ρ Ad) a = 0 a = ( ρAd) a = ( ρAd)
a = a + a + a + a
E e W N n S s
P W E S N
* * *
( ρ ) ( ρ ) ( ρ ) ( ρ )
b= uA − u A + v A − u A
wall e s n
Comparing Eq.'s (53)-(54) with (39)-(40) for a near boundary control volume the same
definition of the coefficients as used for the interior points can be used for a near
boundary control volume by setting the corresponding coefficient (a w in this case) to zero
and using u wall in the b term.
The above formulation corresponds to Neumann boundary condition ∂p´/∂n = 0, where n
is normal to the boundary. As a result no value of pressure correction at the boundary
( p′
w
) is involved in this formulation. However, the value of the pressure correction is
needed for correcting the nodal velocities near boundaries. For example, for correcting
the u-velocity at a nodal point P near a west boundary, p′
w
at the west boundary is needed
in accordance with equation (42). This value can be obtained by using ∂p´/∂n = 0 at the
boundary, that is using p′ (1, j) = p′
(2, j)
.
References
Choi S. K., "Note on the Use of Momentum Interpolation <strong>Method</strong> for Unsteady Flows",
Numerical. Heat Transfer Part, A, vol. 36, pp. 545-550, 1999.
Majumdar S., "Role of Underrelaxation in Momentum Interpolation for Calculation of
Flow with Nonstaggered Grids", Numerical Heat Transfer, Part B, vol. 13, pp. 125-132,
1988.
Rhie C. M. and Chow W. L., "Numerical Study of the Turbulent Flow Past an Airfoil
with Trailing Edge Separation", AIAA Journal, vol. 21, no 11, pp. 1525-1535, 1983.
Yu B., Tao W., and Wei J., "Discussion on Momentum Interpolation <strong>Method</strong> for
Collocated Grids of Incompressible Flow", Numerical. Heat Transfer Part B, vol. 42, pp.
141-166, 2002.
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