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> (see [[LES filters]]), |
<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>. | which is taken as a Dirac delta <math> \psi_\eta \equiv \delta ( \xi - \eta ) </math>. |
Revision as of 15:19, 14 November 2005
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, conditional density-weighted (Favre) filtering is used, ,