On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

Abstract

We assess the performance of a high-order discontinuous Galerkin (DG) approach to simulate wall-bounded turbulent flows for a range of Reynolds numbers. First, a plane channel flow configuration with turbulent heat transfer at Re τ = 640 is considered. Second, a detached flow configuration is investigated. This configuration represents the flow over periodically arranged hills. Four bulk Reynolds numbers Re b are considered: 2 800, 10 595, 19 000, and 37 000. For Re b = 2 800 direct numerical simulation (DNS) is used. Large-eddy simulations (LES) based on the WALE subgrid-scale model are carried out for the higher Re b . The simulation results are compared to reference data from CFD and experiment. hp-convergence analyses are performed which demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this work that the use of a subgrid modelling approach together with local hp-adaptation could greatly improve the accuracy of the solution without penalising the computational cost of the simulation.

Large Eddy Simulation Requirements for the Flow over Periodic Hills

“…A very good compliance is obtained for the mean velocity components. The u -profiles obtained on the finest grid (512 × 256 × 256) are closer to the DG ones [75] than to those of the RT-LES with 256 × 128 × 128 points. Small discrepancies are noted for the vertical velocity profiles at x/ h = 2 and 6 with PIV measurements.…”

“…Small discrepancies are noted for the vertical velocity profiles at x/ h = 2 and 6 with PIV measurements. At these locations, the 256 × 128 × 128 RT-LES is closer to the experimental points, and the 512 × 256 × 256 RT-LES is closer to the DG-LES [75]. The LES with the 512 × 256 × 256 grid is however in better agreement with PIV data than other LES at x/ h = 8, which was identified as a location sensitive to grid refinement.…”

“…Similarly, using multiscale models significantly improves solution quality, although the results are not more accurate than those obtained with the RT strategy alone. The activity of eddy-viscosity SGS models is well illustrated experiments Rapp & Manhart [24]; DG LES of de la Llave Plata et al [75]. Mean streamwise u a and vertical v b velocities the dominant role played by numerical filtering.…”

“…Figures 20 and 21 show profiles at different streamwise stations for the mean velocity components and the turbulent intensities, respectively. The profiles are compared with the PIV measurements at Re=19 000 of Rapp and Manhart [24] and with the recent compressible Discontinuous Galerkin (DG) simulation of de la Llave Plata et al [75]. The latter performed LES with WALE model and the DG method with a polynomial approximation of degree 3 (DG-p3 of order 4).…”

A Discontinuous Galerkin Variational Multiscale Approach to LES of Turbulent Flows

“…The simulation results presented here have been performed using the compressible DG solver Aghora developed at ONERA described in [1,2]. The DG discretization is based on a modal approach, and over-integration is performed for de-aliasing purposes.…”