A Comprehensive Study About Implicit/Explicit Large-Eddy Simulations with Implicit/Explicit Filtering

A high-order computational fluid dynamics code was developed to simulate the compressible Taylor–Green vortex problem by means of large-eddy (LES) and direct numerical simulations. The code, BASIC, uses explicit central-differencing to compute the spatial derivatives and explicit low storage Runge–Kutta methods for the temporal discretization. Central-differencing schemes were combined with relaxation filtering or with splitting formulas to discretize convective derivative operators. The application of split forms to convective derivatives generally guarantees good stability properties with marginal dissipation. However, these types of schemes were found to be unsuited to perform implicit large-eddy simulations (ILES). The minimally dissipative schemes showed acceptance performance, only when combined with a sub-grid scale model. The relaxation-filtering strategy, on the other hand, although more dissipative, was proven to be more adequate to perform ILES. We showed that reducing the filter dissipation, by optimizing its damping function, has a positive impact in the flow solution. When performing ILES, the utilization of split formulas in conjunction with relaxation filtering has equally yielded promising results. This combined approach enhances numerical stability while preserving low levels of numerical dissipation.