Academia.eduAcademia.edu

Figure 6 – uploaded by Pablo Fernandez

See full PDFdownloadDownload figure
Figure 7: One-dimensional kinetic energy spectrum in the Taylor-Green vortex at Re = 1600 and t = 8L/Vo (left), and Re = co and t = 9L/Vo (right) for ILES, static Smagorinsky, dynamic Smagorinsky and Vreman. The WALE model led to nonlinear instability and the simulation breakdown at t = 4.59 L/Vo and 2.75 L/Vo in the viscous and inviscid cases, respectively. Figure 6: Snapshot of vorticity norm ||w|| £/Vo on the periodic plane x = —L7 of the viscous Taylor-Green vortex at t = 8L/Vo. Left to right: ILES, static Smagorinsky, dynamic Smagorinsky and Vreman. The WALE model led to nonlinear instability and the simulation breakdown at t © 4.59 L/Vo.

Figure 7 One-dimensional kinetic energy spectrum in the Taylor-Green vortex at Re = 1600 and t = 8L/Vo (left), and Re = co and t = 9L/Vo (right) for ILES, static Smagorinsky, dynamic Smagorinsky and Vreman. The WALE model led to nonlinear instability and the simulation breakdown at t = 4.59 L/Vo and 2.75 L/Vo in the viscous and inviscid cases, respectively. Figure 6: Snapshot of vorticity norm ||w|| £/Vo on the periodic plane x = —L7 of the viscous Taylor-Green vortex at t = 8L/Vo. Left to right: ILES, static Smagorinsky, dynamic Smagorinsky and Vreman. The WALE model led to nonlinear instability and the simulation breakdown at t © 4.59 L/Vo.

Related Figures (20)

Figure 1: Time evolution of kinetic energy dissipation rate in the Taylor-Green vortex at Re = 1600 (left) and Re = © (right) for the Riemann solvers considered.
Figure 1: Time evolution of kinetic energy dissipation rate in the Taylor-Green vortex at Re = 1600 (left) and Re = © (right) for the Riemann solvers considered.
Figure 2: Time evolution of numerical dissipation of kinetic energy, as defined in Eq. (4), in the Taylor-Green vortex at Re = 1600 (left) and Re = oo (right) for the Riemann solvers considered.
Figure 2: Time evolution of numerical dissipation of kinetic energy, as defined in Eq. (4), in the Taylor-Green vortex at Re = 1600 (left) and Re = oo (right) for the Riemann solvers considered.
Table 2: Average absolute-value jump across elements on the periodic plane « = —Lm of the Taylor-Green vortex at Re = 1600 and t = 8L/V. Table 1: Average absolute-value jump across elements on the periodic plane « = —Lm of the Taylor-Green vortex at Re = 1600 andt =3L/V.
Table 2: Average absolute-value jump across elements on the periodic plane « = —Lm of the Taylor-Green vortex at Re = 1600 and t = 8L/V. Table 1: Average absolute-value jump across elements on the periodic plane « = —Lm of the Taylor-Green vortex at Re = 1600 andt =3L/V.
Table 4: Average absolute-value jump across elements on the periodic plane « = —Lz of the Taylor-Green vortex at Re = oo andt =8L/Vo. Table 3: Average absolute-value jump across elements on the periodic plane x = —Lm of the Taylor-Green vortex at Re = oo and t=3L/VW.
Table 4: Average absolute-value jump across elements on the periodic plane « = —Lz of the Taylor-Green vortex at Re = oo andt =8L/Vo. Table 3: Average absolute-value jump across elements on the periodic plane x = —Lm of the Taylor-Green vortex at Re = oo and t=3L/VW.
Figure 3: One-dimensional kinetic energy spectrum in the Taylor-Green vortex at Re = 1600 and t = 8L/Vo (left), and Re = oo and t = 9 L/Vo (right) for the Riemann solvers considered.
Figure 3: One-dimensional kinetic energy spectrum in the Taylor-Green vortex at Re = 1600 and t = 8L/Vo (left), and Re = oo and t = 9 L/Vo (right) for the Riemann solvers considered.
Figure 4: Time evolution of kinetic energy dissipation rate in the Taylor-Green vortex at Re = 1600 (left) and Re = o0 (right) for ILES, static Smagorinsky, dynamic Smagorinsky, WALE and Vreman LES.
Figure 4: Time evolution of kinetic energy dissipation rate in the Taylor-Green vortex at Re = 1600 (left) and Re = o0 (right) for ILES, static Smagorinsky, dynamic Smagorinsky, WALE and Vreman LES.
Figure 5: Time evolution of volume-averaged dynamic Smagorinsky constant in the Taylor-Green vortex. Note C; = 0.16 in static Smagorinsky [34].
Figure 5: Time evolution of volume-averaged dynamic Smagorinsky constant in the Taylor-Green vortex. Note C; = 0.16 in static Smagorinsky [34].
not exactly agree with the target Re, (denoted by Re!*"9**) if the resolution is not sufficiently fine to matck the wall stress in DNS. This will be the case at Re'“"9*' = 544 and, for some of the explicit models, also at 182. Table 5: Distance between high-order nodes (in wall units) for turbulent channel flow. Aysug denotes the average distance along the wall-normal direction. Ay, denotes the distance from the wall to the first high-order node along the wall-normal direction.
not exactly agree with the target Re, (denoted by Re!*"9**) if the resolution is not sufficiently fine to matck the wall stress in DNS. This will be the case at Re'“"9*' = 544 and, for some of the explicit models, also at 182. Table 5: Distance between high-order nodes (in wall units) for turbulent channel flow. Aysug denotes the average distance along the wall-normal direction. Ay, denotes the distance from the wall to the first high-order node along the wall-normal direction.
Figure 8: Mean velocity profile in turbulent channel flow at Re!*"9*' = 182 (left) and 544 (right) for the Riemann solvers considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization.
Figure 8: Mean velocity profile in turbulent channel flow at Re!*"9*' = 182 (left) and 544 (right) for the Riemann solvers considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization.
Figure 9: Reynolds stresses in turbulent channel flow at Re%*"9*' = 182 for the Riemann solvers considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization.
Figure 9: Reynolds stresses in turbulent channel flow at Re%*"9*' = 182 for the Riemann solvers considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization.
Table 6: Values of Re£”5 computed from the wall friction in the LES simulations.
Table 6: Values of Re£”5 computed from the wall friction in the LES simulations.
Figure 10: Mean velocity profile in turbulent channel flow at Re'*"9*! = 182 for the SGS models considered. Inner (based on the wall friction in the simulation) and outer boundary layer scales are used for non-dimensionalization in the left and right figures, respectively.
Figure 10: Mean velocity profile in turbulent channel flow at Re'*"9*! = 182 for the SGS models considered. Inner (based on the wall friction in the simulation) and outer boundary layer scales are used for non-dimensionalization in the left and right figures, respectively.
Figure 11: Mean velocity profile in turbulent channel flow at Re'*"9*' = 544 for the SGS models considered. Inner (based on the wall friction in the simulation) and outer boundary layer scales are used for non-dimensionalization in the left and right figures, respectively.
Figure 11: Mean velocity profile in turbulent channel flow at Re'*"9*' = 544 for the SGS models considered. Inner (based on the wall friction in the simulation) and outer boundary layer scales are used for non-dimensionalization in the left and right figures, respectively.
Figure 12: Reynolds stresses in turbulent channel flow at Re’@"9*' = 182 for the SGS models considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization. The color legend is shown in Figures 10 and 11.
Figure 12: Reynolds stresses in turbulent channel flow at Re’@"9*' = 182 for the SGS models considered. The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization. The color legend is shown in Figures 10 and 11.
Figure 14: Resolved eddy viscosity (top) and total eddy viscosity (bottom) in turbulent channel flow at Re%*"9 = 182 (left) and 544 (right) for the SGS models considered. The definition of these eddy viscosities is given in Eq. (7). The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization. Figure 13: Dynamic Smagorinsky constant in turbulent channel flow at Re{“"9*' = 182 and 544. Note C, = 0.16 in static Smagorinsky [34].
Figure 14: Resolved eddy viscosity (top) and total eddy viscosity (bottom) in turbulent channel flow at Re%*"9 = 182 (left) and 544 (right) for the SGS models considered. The definition of these eddy viscosities is given in Eq. (7). The wall friction in the simulations is used to compute the near-wall velocity and length scales for non-dimensionalization. Figure 13: Dynamic Smagorinsky constant in turbulent channel flow at Re{“"9*' = 182 and 544. Note C, = 0.16 in static Smagorinsky [34].
where : denotes the Frobenius inner product of two matrices. We finally define several inner products associated with these finite element spaces. In particular, given Ww, e vi, W,VeE oF and 7,¢ € Mt, we write where €} is a subset of €,. Different choices of €/ lead to different discretization methods within the hybridized DG family that have different properties in terms of accuracy, stability, and number of globally coupled unknowns [21, 61]. In particular, the HDG, EDG and IEDG methods are obtained by setting EF = 0, EF = & and EF = Ef, respectively.
where : denotes the Frobenius inner product of two matrices. We finally define several inner products associated with these finite element spaces. In particular, given Ww, e vi, W,VeE oF and 7,¢ € Mt, we write where €} is a subset of €,. Different choices of €/ lead to different discretization methods within the hybridized DG family that have different properties in terms of accuracy, stability, and number of globally coupled unknowns [21, 61]. In particular, the HDG, EDG and IEDG methods are obtained by setting EF = 0, EF = & and EF = Ef, respectively.
Related topics:
Finite Element MethodsDiscontinuous Galerkin MethodsLarge Eddy SimulationTurbulent Flows
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved