Large Eddy Simulation - Filter Definition and Properties

Filter Definition and Properties

An LES filter can be applied to a spatial and temporal field and perform a spatial filtering operation, a temporal filtering operation, or both. The filtered field, denoted with a bar, is defined as:

$\overline{\phi(\boldsymbol{x},t)} = \displaystyle{ \int_{-\infty}^{\infty}} \int_{-\infty}^{\infty} \phi(\boldsymbol{r},t^{\prime}) G(\boldsymbol{x}-\boldsymbol{r},t - t^{\prime}) dt^{\prime} d \boldsymbol{r}$

where is the filter convolution kernel. This can also be written as:

$\overline{\phi} = G \star \phi .$

The filter kernel has an associated cutoff length scale and cutoff time scale . Scales smaller than these are eliminated from . Using the above filter definition, any field may be split up into a filtered and sub-filtered (denoted with a prime) portion, as

$\phi = \bar{\phi} + \phi^{\prime} .$

It is important to note that the large eddy simulation filtering operation does not satisfy the properties of a Reynolds operator.

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