Following Strelets [58], the zonal DES model switches from
a second-order upwind scheme in the RANS region to a central difference
scheme in the LES region. The finite volume method approximates the
advection term in the transport equation for a generic variable 
as:
 | (2–200) |
where 
is
the control volume value, the index 
denotes
the integration points on the control volume faces, 
and 
are the mass flow and the transported variable value
estimated at the integration point 
. The
value of 
is obtained by interpolating from the surrounding
mesh nodes according to the selected discretization scheme. Blending
between the upwind-biased scheme and the central scheme is achieved
by combining the corresponding interpolation values 
and 
using the
blending function 
:
 | (2–201) |
A specific form of the blending function 
is taken from
Strelets [58] with only minor changes:
 | (2–202) |
 | (2–203) |
 | (2–204) |
with 
being
the maximum neighboring mesh edge, and the same constant values as
in Strelets [58]:
 | (2–205) |
Note: For the SST-DES model, the blending function 
is
additionally limited in order to prevent the mesh-induced separation:
 | (2–206) |
where F1 and F2 are the first and second SST blending function 
and 
([129]), respectively.
BF1 and BF2 are blend factors and are used in order to select one
of the two blending functions. The default and the recommendation
is to use the second SST blending function F2, therefore the corresponding
default values are BF1 = 0 and BF2 = 1.
A limiter based on the Courant-number has been developed in
order to avoid oscillations due to the central difference scheme,
which can occur for medium and high Courant-numbers (this limiter
is not given in the original formulation of Strelets [58]).
The blending function 
is limited in the following way:
 | (2–207) |
The default values of 
and 
are 5.0 and 1.0, respectively.
The blending function, 
, is available in CFD-Post and allows you
to distinguish between the regions in the flow where the advection-scheme
is user-specified (upwind-biased) or the central difference scheme
is used. The corresponding variable name in CFD-Post is Blending Function for DES model.
According to Equation 2–201, the value of the variable
is 1 to denote the user-specified advection scheme
and 0 for the central difference scheme. Therefore,
a value of 1 typically denotes the RANS region
using an upwind-biased scheme and a value of 0 denotes the LES region using the central-difference scheme. However,
if the choice of the user-specified advection scheme is central difference,
then the Blending Function for DES model returns
a value of 1 everywhere.
For SDES and SBES models, the default value of constant 
of Equation 2–203 is 0.4. This constant is available in CFX-Pre as CCL parameter Csdes for Numerical Blending. Reducing the value of this constant results in lower weighting of the upwind-biased scheme.