Commutator-errors in large-eddy simulation

A new formulation is derived for the commutator-errors in large-eddy simulation of incompressible flow. These commutator-errors arise from the application of non-uniform filters to the Navier-Stokes equations. As a consequence, the filtered velocity field is no longer solenoidal. The order of magnitude of the commutator-errors is compared with the divergence of the turbulent stresses. This shows that one can not reduce the size of the commutator-errors independently of the turbulent stress terms by some judicious construction of the filter operator. Similarity modeling for the commutator-errors is presented, including an extension of Bardina's approach and the application of Leray regularization. The performance of the commutator-error parameterization is illustrated with the one-dimensional Burgers equation. For large filter-width variations the Leray approach is shown to capture the filtered flow with better accuracy than is possible with Bardina's approach.