Conditional filtering
From CFD-Wiki
A conditional filtering operation of a variable is defined as
where is a positive defined space filter with filter width
(see LES filters),
is a fine-grained probability density function,
which is taken as a Dirac delta
.
The probability density function
is a subgrid PDF and
is the sample space of the passive scalar
.
In variable density flows, the conditional density-weighted (Favre) filtering is used.
Using the density-weighted PDF ,
, the conditionally Favre filtered operation is
The relation between Favre and conventional PDF's is