Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Abstract

Solving two-dimensional compressible turbulence problems up to a resolution of 16, 384 2 , this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes.

An Open and Parallel Multiresolution Framework Using Block-Based Adaptive Grids

“…In both density and vorticity field one can observe small scale structures created by the shear layer instability. The size and form of the structures are in agreement with [17].…”

“…In this section we present the results of a second test case, governed by the ideal-gas, constant heat capacity compressible Navier-Stokes equations in the skew-symmetric formulation [21]. A double shear-layer in a periodic domain is perturbed so that the growing instabilities end up with small scale structures, similar to [17]. The size of the computational domain is L = L x = L y = 8 and the shear layer is initially located at L 2 ± 0.25.…”

A localised dynamic closure model for Euler turbulence

“…The instability is triggered through the growing discontinuous wave (sharp density or discontinuous velocity) at the interface which induces vorticity and eventually transitions into a turbulent field through nonlinear interactions or mixing. The evolution of this instability can be compared across different numerical schemes through the simulation results to give a qualitative and quantitative measurement on the performance of that model (Maulik and San 2017;San and Kara 2015). In our study, we use the averaged kinetic energy spectra and density contour to assess the models statistically and visually.…”

“…Among all the high order shock-capturing algorithms, upwind-biased and nonlinearly weighted approaches (e.g., Weighted Essentially Non-Oscillatory (WENO) scheme) are widely used in considerable amount of works because of their robustness to capture discontinuities in shock dominated flows and high order of accuracy in preserving turbulence features (Yamamoto and Daiguji 1993;Martín et al 2006;Titarev and Toro 2005;Pirozzoli 2011;Zhang, Shu, and Zhou 2006). The implicit large eddy simulation (ILES) framework utilizes shock-capturing schemes very frequently where the numerical dissipation is added through an upwinding scheme (Maulik and San 2017;Zhou et al 2014;Karaca, Lardjane, and Fedioun 2012). ILES has been successfully applied to complex flows in engineering and physical applications as an approach to simulate high (Re) flows with computational efficiency (Zhao, Lardjane, and Fedioun 2014;Grinstein, Margolin, and Rider 2007;Watanabe et al 2016;Zhou and Thornber 2016;Domaradzki, Xiao, and Smolarkiewicz 2003).…”

Stratified Kelvin-Helmholtz turbulence of compressible shear flows

“…We utilize a parallel approach for the computational solution of our governing laws implemented in the OpenMPI framework. Details about implementation and the computational performance of our solver may be found in Maulik and San (2017) additionally showing weak and strong scaling tests. Our three-dimensional simulations employ a similar approach.…”