On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

Abstract

High-speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non-Oscillatory (WENO) schemes due to their high-order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence-resolving simulations. In this connection, the recently developed Targeted Essentially Non-Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re τ = 222 is conducted using OpenSBLI, a high-order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high-order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three-dimensional vortical structures. The sixth-order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth-and sixth-order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.

Direct numerical simulation of compressible turbulence in a counter-flow channel configuration

“…The streamwise and spanwise boundaries are periodic, while isothermal (T w = 1.0) no-slip walls are assigned to the boundaries in the normal direction (y). In order to accurately resolve the near wall region, the grid is stretched in the y direction using a stretching function with a stretching factor of 1.7 as discussed in [25]. A tangent hyperbolic forcing function is used to drive the flow in opposite directions on the upper and lower halves of the channel.…”

“…Unless otherwise stated, simulations are initialized using an approach originally developed for DNS of conventional channel flows as discussed in [25]. Specifically, fluctuations based on sine and cosine disturbances are superimposed over a mean classical turbulent velocity profile in the x direction and in other directions only the sine and cosine disturbances are imposed.…”

OpenSBLI: Automated code-generation for heterogeneous computing architectures applied to compressible fluid dynamics on structured grids

“…These applications include supersonic laminar SBLI [50], laminar duct SBLI with sidewalls [51], transitional duct SBLI with sidewalls [52], and hypersonic roughness-induced transition at Mach 6 [53]. The numerical schemes in OpenSBLI have also been assessed and validated for supersonic Taylor-Green vortex cases [33], and supersonic turbulent channel flows [54].…”

“…To introduce upstream disturbances to the otherwise laminar SBLI, modal time-dependent forcing is applied as an acoustic body-forcing term in the continuity equation (1). The forcing takes the form ρ = A exp − (x − x F ) 2 + (y − y F ) 2 cos (βz) sin (ωt) , (54) for an amplitude A = 2.5 × 10 −3 , frequency ω = 0.1011, and wavenumber β = 0.23. This single mode corresponds to the most unstable mode obtained from linear stability analysis of a laminar separation bubble [60].…”

A Filtered Embedded Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Law

“…The third strategy introduces a methodology to switch the scheme between the nonlinear and linear schemes, which can combine the low dissipation of linear scheme and stability of nonlinear scheme. Representatively, the targeted ENO(TENO) scheme introduced by Fu et al [11] is applicable for the simulation involving a wide range of flow scales [12,13] . However, due to its relatively direct switching strategy between linear and nonlinear scheme, the computational stability in the calculation needs to be considered.…”