On the performance of a high-order multiscale DG approach to LES at increasing Reynolds number

Abstract

The variational multiscale (VMS) approach based on a high-order discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds 3 900, 20 000 and 140 000. The effect of the numerical flux function on the quality of the LES solutions is also studied in the context of very coarse discretizations of the TGV configuration at Re = 20 000. The potential of using p-adaption in combination with DG-VMS is illustrated for the cylinder flow at Re = 140 000 by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy [59]. The results from these tests demonstrate the robustness of the DG-VMS approach with increasing Reynolds number on a highly curved geometrical configuration.

Dynamical p−adaptivity for LES of compressible flows in a high order DG framework

“…[18,37,42,35,24,43]. For statistically steady state configurations, statically p−adaptive LES was shown in [13,40,44,38] to lead to significant efficiency gains, while an example of dynamical p−adaptation is described in [36] in an ILES context.…”

Dynamical p-adaptivity for LES of compressible flows in a high order DG framework

“…Furthermore, p−adaptive techniques are appealing, since they allow to correct possible shortcomings of the computational mesh as well as to perform dynamically adaptive simulations without extensive remeshing. Static polynomial adaptivity has been applied to LES in a DG context in [10,34,24,31]. An essential tool for such simulations is an adaptation criterion that, rather than simply increasing the resolution in order to decrease the error, which is known to lead to a DNS solution [23,29], tries instead to adjusting the resolution in order to directly resolve only a prescribed amount of the turbulent scales.…”

“…Furthermore, p−adaptive techniques are appealing since they allow to correct possible shortcomings of the computational mesh, as well as to perform dynamically adaptive simulations without extensive remeshing. Static polynomial adaptivity was applied to LES in [10,34,24,31] to efficiently simulate statistically steady phenomena, while an example of dynamical adaptation is described in [11] in an ILES context.…”

hp -adaptive hybrid RANS/LES simulations for unstructured meshes with the discontinuous Galerkin method

“…According to Sagaut et al in [61] the DES approach can be considered analogous to the well-known Smagorinsky model for free-shear flows, and a value of 𝐶 𝐷𝐸𝑆 = 0.65 is equivalent to the Smagorinsky constant 𝐶 𝑆 ≃ 0.2. Due to the intrinsic dissipation of DG methods, a lower 𝐶 𝑆 = 0.1 is often employed [42] for LES/DG simulations. We could think that decreasing the constant to 𝐶 𝐷𝐸𝑆 = 0.3 or 0.4 would be an appropriate choice to allow the subgrid model to provide a sufficient amount of dissipation, without over-dissipating the turbulent structures.…”

“…In the literature we can find adaptive strategies based on a posteriori error estimation aimed at LES/ILES simulations performed in the context of p-adaptive DG methods. Static unsteady p-adaptation was performed by Chapelier et al [41], de la Llave et al [42], Noventa et al [43] and Bassi et al [44], while Abbà et al [45] followed a dynamic approach.…”