Commutation error in LES with time-dependent filter width

This paper presents an investigation of the possible commutation errors arising in Large Eddy Simulations performed with a filter width which varies in time, e.g. when the grid/spectral resolution is modified dynamically during the computations. Some theoretical developments provide an explicit expression for this error, which is shown to depend explicitly on the filter kernel properties, and on the time derivative of the cut-off length. From this analysis, some constraints on the filter kernel are derived in order to minimize the error. The particular case of a Gaussian filter is considered, which yields to a first error term. Finally, the dependency of the temporal commutation error to the variations of the filter width is investigated by performing a priori tests in the case of isotropic homogeneous turbulence with a varying cut-off length.