On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence
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- 作者：R.C. Moura ; r.moura13@imperial.ac.uk ; G. Mengaldo ; J. Peiró ; S.J. Sherwin
- 关键词：Implicit LES ; Under-resolved DNS ; Dispersion&ndash ; diffusion analysis ; High-order discontinuous Galerkin ; Inviscid Taylor&ndash ; Green vortex ; Euler turbulence
- 刊名：Journal of Computational Physics
- 出版年：2017
- 出版时间：1 February 2017
- 年：2017
- 卷：330
- 期：Complete
- 页码：615-623
- 全文大小：1401 K
- 卷排序：330
文摘
We present estimates of spectral resolution power for under-resolved turbulent Euler flows obtained with high-order discontinuous Galerkin (DG) methods. The ‘1% rule’ based on linear dispersion–diffusion analysis introduced by Moura et al. (2015) [10] is here adapted for 3D energy spectra and validated through the inviscid Taylor–Green vortex problem. The 1% rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra. As the original rule relies on standard upwinding, different Riemann solvers are tested. Very good agreement is found for solvers which treat the different physical waves in a consistent manner. Relatively good agreement is still found for simpler solvers. The latter however displayed spurious features attributed to the inconsistent treatment of different physical waves. It is argued that, in the limit of vanishing viscosity, such features might have a significant impact on robustness and solution quality. The estimates proposed are regarded as useful guidelines for no-model DG-based simulations of free turbulence at very high Reynolds numbers.