 Grid filter

A grid filter defines the resolved field associated with a large eddy simulation, commonly written $\bar{u}=G_{\Delta }\ast u$. Its name reflects the connection between resolved scales and a computational grid, but the filtering operator and the mesh are different specifications. An explicit spatial averaging filter states its kernel; in other methods the retained representation and numerical operations supply an implicit scale selection.^[ref]

A characteristic width is often related to cell dimensions. One possible three-dimensional convention isCells with widths $0.01$, $0.02$ and $0.04\mathrm{m}$ then have $\Delta =0.02\mathrm{m}$. This single number preserves the volume scale but does not describe the strong directional differences of the cell. The filter shape and directional resolution still matter.

Sampling alone also cannot determine which unresolved oscillations were present. At eight equally spaced points on a periodic interval of length $L$, the modes with indices ten and two have identical sine samples:This is aliasing. Removing the high mode by a specified filter before sampling and merely sampling the unfiltered field are different operations.

The subgrid-scale stress depends on the filter actually adopted. A test filter then applies an additional operation to the already resolved data. Reporting only a grid spacing, without the filtering and discretization choices, can leave the mathematical meaning of the resolved field and its closure ambiguous.