Discrete filter operators for large-eddy simulation using high-order spectral difference methods

Introduction
Because of the continuous and growing development of available computational resources during the last decade, there has been an increased interest in the use of large-eddy simulation (LES) for simulating engineering flows of practical interest. Many engineering applications—for example, those involving vortex-dominated flow dynamics, transitional or massively detached flows, turbulent mixing and combustion, or aerodynamic noise—require the numerical simulation of flows over complex geometries with a level of detail that the most widely used Reynolds averaged Navier–Stokes (RANS) simulations cannot fulfill. For such applications, LES represents the most efficient approach.

Notwithstanding the considerable effort that has been devoted to the development of accurate and relatively reliable sub-grid scale (SGS) models for LES, in most cases, the underlying numerical methods available within the framework of industrial CFD applications rely upon highly dissipative schemes. The inherent numerical dissipation introduced by such numerical schemes limits their ability to correctly represent the high frequency range of the spectrum of turbulence. On the other hand, caution should be exercised when using less dissipative high-order numerical methods to perform implicit LES without any SGS model, namely compute a truncated turbulent spectrum designating whatever amount of numerical dissipation method brought by the numerical scheme to set small-scale dissipation. Depending on the problem under study and the grid resolution used in the computation, it is uncertain whether such an approach would produce accurate and useful results. In fact, numerical dissipation can supposedly handle dissipative processes, which are confined to small scales, but can certainly not reproduce complex interactions between large and small scales, which are often observed in LES.
Authors:
Guido Lodato/Patrice Castonguay/Antony Jameson


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