Large Eddy Simulation

Large Eddy Simulation (LES) in NekRS uses a filter to drain energy from the lowest resolved wavelengths. This filter essentially acts as a sub-grid scale dissipation model. NekRS contains two options for filters, both of which exhibit spectral convergence. Both options use the same underlying convolution operator, but apply it in different ways. This documentation page is an abridged version of the Nek5000 filtering documentation.

The solution in NekRS is represented on each element using a polynomial basis (Lagrange polynomials, ). For example, in a 1-D element, the solution is

where are coefficients. A filtered version of , or , can then be represented as

where are weighting factors, are the Legendre polynomials, and are coefficients. In other words, the nodal solution (Lagrange basis) is first interpolated to the modal Legendre basis, the filtering is applied there, and then interpolated back.

Typically, is unity for certain values of so as to only apply the filter to the highest-frequency modes (),

We denote the convolution operator which represents applying the 1-D filtering operation to all three dimensions as , such that

Note that because the depend on the local element size, the filtering operation is not uniform across the entire domain. Generally, you should use as minimal a filter as possible while maintaining stability (though due to the spectral convergence, if you use a stronger setting you will still converge in the limit of increasing polynomial order).