# Subgrid PDF

### From CFD-Wiki

(Difference between revisions)

m |
m |
||

Line 42: | Line 42: | ||

:<math> | :<math> | ||

\bar{\rho} \tilde{P}(\underline{\psi}) | \bar{\rho} \tilde{P}(\underline{\psi}) | ||

- | \equiv \int_V | + | \equiv \int_V \rho |

- | \prod_i^N | + | \prod_i^N \delta \left( \Phi_j(\mathbf{x'},t) - \psi_j \right) |

G \left( \mathbf{x} -\mathbf{x'}, \Delta \right) dV' | G \left( \mathbf{x} -\mathbf{x'}, \Delta \right) dV' | ||

</math> | </math> |

## Revision as of 12:30, 8 May 2006

A subgrid probability density function , also known as filtered density function (FDF), is the distribution function of scalar at subgrid scales.

The probability of observing values between within the filter volume is

where is the Dirac delta function, is a positive defined filter function with filter width .

The joint subgrid PDF of scalars is

where is the phase space for the scalar variables .

A density weighted FDF, , can be obtained as

and in the same manner for the joint FDF