Numerical simulations for turbulent flows using the most promising methodology, Large Eddy Simulation (LES), are grid-spacing and discretization-order dependent. This means that the solution is not trustworthy and cannot be compared with experiments to determine the validity of the mathematical model.
A methodology was developed to produce discretization-order independence for some grid spacings and grid-spacing independence for some discretization orders. To this end, the nonlinear terms in the equations were filtered with an explicit filter to remove the small scales created during the simulation. The explicitly filtered Large Eddy Simulation (EFLES) formulation that has been previously developed and examined for compressible single-phase flows has been formulated and assessed anew for two-phase flows with phase change. Similar to the single-phase EFLES formulation, the small-scale-producing nonlinear terms in the governing equations are explicitly filtered, and this procedure is applied both to the differential equations and to the equation of state.
Examination of these results revealed that unlike for conventional LES where the results are always grid-dependent, the EFLES results are grid-independent for sufficiently large filter-width to grid-spacing ratio. The EFLES results were independent of the drop-field SGS (subgrid scale) models used for the range examined here. The filter-width to grid-spacing ratio required to obtain grid-independent results is the same for the two-phase case compared to the single-phase case for the two lower-order discretizations, but larger by a factor of two for the eighth-order discretization, and moreover, in contrast to the single-phase case, the coarse grid does not converge for the eighth-order discretization. This different result was explained by the increased complexity of two-phase flows, even at scales larger than the filter, compared to single-phase flows.