Advanced numerics in fluid mechanics for virtual prototyping of energetic systems: High-order schemes for high-fidelity LES of complex geometries – ANVES

The Spectral Difference (SD) scheme, a high-order discontinuous finite element method for unstructured meshes, enables extremely accurate simulations of complex geometries with minimal dissipation, relatively low algorithmic complexity and optimal scalability on multi-processor environments. A preliminary study within the ANVES project has highlighted the benefit of using the high-order SD discretization for an accurate representation of turbulent phenomena (namely, transitional and wall-bounded turbulence), but also the necessity to combine this approach with a dynamic LES model or an appropriate regularization technique, which would activate only where needed to recover physically consistent results (e.g., in regions where fully developed turbulence is present or where the numerical dissipation is not sufficient).
Such a model is conceived as a fully integrated dissipative term which selectively injects the correct amount of sub-grid scale dissipation depending on the order of the simulation and the actual resolution of the mesh.

A new Spectral-Element Dynamic Model (SEDM) for LES has been developed. The model is suitable for discontinuous finite element methods and features the ability to locally adapt the amount of sub-grid dissipation thanks to a “turbulence” or “resolution” sensor. This sensor—which leverages available modal information within the discretization elements—is built as a function of the energy power decay in Legendre space. This function is coupled to a simple expression for the eddy-viscosity which guarantees the correct amount of sub-grid dissipation in the case of high Reynolds number fully developed turbulence. This approach is relatively simple compared to existing dynamic approaches, as no explicit filtering, clipping or smoothing is required in order to obtain a robust model. Extensive testing and validation has been carried out on canonical flow cases (homogeneous isotropic turbulence and turbulent channel flow).
The SEDM approach is able to detect the actual (modal) resolution of the flow and hence has the ability to auto-compensate according to the numerical dissipation of the scheme. In a sense, phenomena of error cancellation between the scheme and the LES model are not possible, as the SEDM is numerical-dissipation-aware. The particular formulation of the SEDM makes it immediately applicable on a broad class of discontinuous finite element methods. An extremely broad impact is hence expected in academic and engineering applications involving LES of fully developed or transitional turbulence.

The built-in modal sensor of the SEDM is designed to detect the onset of insufficiently resolved turbulence within the flow. As a result, the model is automatically switched on only where it is needed. In conjunction with the high-order nature of the SD scheme and the relevant minimal dissipation, accurate LES with the richest possible turbulent spectra can be performed. Applications of the SEDM to transitional turbulence are already under way. Additionally, the SEDM sensor can be used, in principle, as a turbulence detector in the near-wall regions. Such an approach, already under study, would allow wall-modeled LES of transitional boundary layers.

Two journal papers on Computers & Fluids and Journal of Computational Physics (one published and one in press, respectively) and two submitted papers to the ETMM-11 ERCOFTAC Symposium. These publications cover the characterization of the numerical dissipation of the Spectral Difference scheme and the development of the novel Spectral-Element Dynamic Model for Large-Eddy Simulation.

The objective of this project is the development of high-order numerical methods for the computation of turbulent flows over complex geometries. The context is that of discontinuous finite elements methods applied to Large-Eddy Simulation. These methods allow to perform the numerical simulation of turbulent confined flows preserving numerical accuracy regardless of the mesh and the geometry. Specific efforts will be done to develop dedicated selective dissipation operators to be used in conjunction with a similarity term and to couple a detailed description of Reynolds-averaged turbulent boundary layers with large-eddy simulation. In order to allow the use of explicit filtering sub-grid scale modeling approaches, dedicated filtering operators or strategies will be developed for these high-order methods on a general class of simplex element types.