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, ,