COMPARISON OF NUMERICAL SCHEMES IN LARGE-EDDY SIMULATION OF THE TEMPORAL MIXING LAYER

A posteriori tests of large-eddy simulations for the temporal mixing l ayer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tenser. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order cent ral difference. The transverse weighting is shown to be necessary, sin ce the standard second-order central difference (A') gives rise to ins tabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulation s with the standard fourth-order central method (B'). Furthermore, a s pectral scheme (C) is tested. Simulations using these schemes have bee n performed for the case where the filter width equals the grid size ( I) and the case where the filter width equals twice the grid size (II) . The filtered DNS results are best approximated in case II for each o f the numerical methods A, B and C. The deviations from the filtered D NS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are sma ller than in case II owing to the smaller filter width, whereas the di scretization error effects are larger, since the flow field contains m ore small-scale contributions. In case I scheme A is preferred over sc heme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the e xpense of a considerably increased computational cost. For the predict ion of some quantities the discretization errors are observed to elimi nate the modelling errors to some extent and give rise to reduced tota l errors.