Subgrid PDF
From CFD-Wiki
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\bar{P}(\underline{\psi}) | \bar{P}(\underline{\psi}) | ||
\equiv \int_V | \equiv \int_V | ||
- | \ | + | \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 12:17, 10 November 2005
A subgrid probability density function
is the distribution function of scalar
at subrid 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