Conditional filtering
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where <math>G </math>is a positive defined space filter with filter width <math> \Delta </math>, | where <math>G </math>is a positive defined space filter with filter width <math> \Delta </math>, | ||
<math> \psi_\eta </math> is a fine-grained [[probability density function]], | <math> \psi_\eta </math> is a fine-grained [[probability density function]], | ||
| + | which is taken as a Dirac delta <math> \psi_\eta \equiv \delta ( \xi - \eta ) </math>. | ||
| + | The probability density function | ||
<math>\bar{P}(\eta) </math> is a [[subgrid PDF]] and <math> \eta </math> is the sample space of the passive scalar | <math>\bar{P}(\eta) </math> is a [[subgrid PDF]] and <math> \eta </math> is the sample space of the passive scalar | ||
<math> \xi </math>. In variable density flows, conditional density-weighted | <math> \xi </math>. In variable density flows, conditional density-weighted | ||
(Favre) filtering is used, | (Favre) filtering is used, | ||
<math> \bar{\rho}_\eta \tilde{\Phi}_\eta=\overline{\rho \Phi|\eta} </math>, | <math> \bar{\rho}_\eta \tilde{\Phi}_\eta=\overline{\rho \Phi|\eta} </math>, | ||
Revision as of 14:39, 11 November 2005
A conditional filtering operation of a variable 
is defined as
where 
is a positive defined space filter with filter width 
,
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, conditional density-weighted
(Favre) filtering is used,
,
