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LES grid resolution requirements for the modelling of gravity currents. (English) Zbl 1410.76112

Summary: The influence of the grid resolution on the large eddy simulation (LES) of a lock-exchange turbidity current is investigated. The simulations are performed using a finite volume Boussinesq code with a Smagorinsky turbulence model for a range of buoyancy Reynolds numbers, ranging from transitional currents (\(\text{Re}_b = 1000\)) to fully-developed turbulence (\(\text{Re}_b = 60,000\)). The general features of the flow and the relative independence of the current front for \(\text{Re}_b > 10,000\) are correctly predicted. In agreement with previous research, the spanwise two-point correlations are found to be the most useful quantities to assess the mesh resolution. In addition, velocity power spectrum densities are used to provide information on the maximum cell size required to ensure the LES filter cutoff wavelength is inside the inertial range of the turbulence spectra. We show that at low Reynolds numbers, the turbulence model is too restrictive and direct resolution (DNS) is preferable. For \(10,000 < \text{Re}_b < 60,000\), the combination of the different criteria lead to a minimum resolution of \(1140 \times 37 \times 74\) cells for coarse LES, and \(1925 \times 62 \times 125\) cells for well-resolved LES, regardless of the Reynolds number. Finally, recommendations are made on how to achieve a well-resolved LES based on examination of the vertical profiles of the ratio of SGS viscosity to molecular viscosity, and of the SGS shear-stress to the resolved Reynolds stress.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics

Software:

TURBINS
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