To validate simulations, one must trust that they are independent of the numerical aspects. A very promising, relatively new methodology for simulating turbulent flows, called Large Eddy Simulation (LES), has some issues in this respect. The issues stem from the aspect that modeling and numerics are totally intertwined, resulting in the fact that the results are grid-dependent and discretization-order-dependent. These issues were described in the preceding article. These issues prevent LES validation with experiments since one can always make adjustments to agree with data, which is not validation.
A new LES formulation has been developed with the goal of obtaining grid-independent results from such computations. The idea is that these results should only depend on the filter width that specifies the smallest scale at which resolved information is desired. Unlike in conventional LES, the small-scale-producing nonlinear terms in the governing equations are explicitly filtered, and this procedure is applied both to the differential equations and the equation of state; this new formulation is called explicitly filtered LES (EFLES). LES was reformulated and shown to be discretization-order independent for a fine grid, and grid-independent for high-order discretization. The re-formulation involves explicit filtering of the conservation equations, whereas in the conventional LES, implicit filtering is used.
The question of whether SGS models are physical or whether their role is uniquely to provide the correct amount of dissipation has also been addressed, and it was concluded that the question is not well posed. Rather, unless a counterexample can be constructed, it appears that these two facets of a model cannot be separated.
Given the importance of grid-independent simulations for model validation with experiments, use of the EFLES formulation is recommended even though it is computationally more intensive than the conventional LES. Just as important, the utilization of a high-order spatial discretization is recommended because the computations can be performed on a coarser grid without impacting the results’ accuracy.