Effect of explicit filter combinations based on symmetric stochastic matrices in direct numerical simulations

Abstract

This study proposes novel conservative filters for uniformly spaced grids. The original conservative filters, proposed by Vreman, are extended by developing a filter matrix that is symmetric stochastic and pentadiagonal, rather than tridiagonal. When the original conservative filters are applied to uniform grids, once the coefficients of the filters at the interior nodes are established, the coefficients of the filter at the boundary can be determined uniquely. This study improves the flexibility of adjusting the filter strength near the boundaries. The numerical results suggest that the developed filters can be applied when it is essential that filters neither increase the global maximum nor decrease the global minimum of a variable.