Abstract
Solving two-dimensional compressible turbulence problems up to a resolution of 16, 3842, 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.
Highlights
The use of nonlinearly weighted and upwind-biased schemes (such as weighted essentially non-oscillatory (WENO) reconstructions) is considered a state-of-the-art numerical tool for the simulation of turbulent compressible flows in the presence of shock waves [1,2,3]. These numerical schemes have an inherent numerical dissipation mechanism due to their asymmetric stencil reconstructions. They are extensively used in the implicit large eddy simulation framework for turbulent flow computation and represent a promising approach to meeting the degree of accuracy required in high precision engineering requirements [4,5,6,7,8]
The main idea of this paper is to examine the relative advantages and disadvantages of these approaches for solving canonical turbulent compressible flow systems including a stratified shear layer instability problem to demonstrate the evolution of linear perturbations into a transition to nonlinear two-dimensional hydrodynamic turbulence
This study presents an in depth analysis of both implicit large eddy simulation (ILES) methods and explicit filtering approaches for the purpose of simulating compressible hydrodynamic turbulence by solving the two-dimensional Euler equations
Summary
The use of nonlinearly weighted and upwind-biased schemes (such as weighted essentially non-oscillatory (WENO) reconstructions) is considered a state-of-the-art numerical tool for the simulation of turbulent compressible flows in the presence of shock waves [1,2,3]. These numerical schemes have an inherent numerical dissipation mechanism due to their asymmetric stencil reconstructions. The main idea of this paper is to examine the relative advantages and disadvantages of these approaches for solving canonical turbulent compressible flow systems including a stratified shear layer instability problem to demonstrate the evolution of linear perturbations into a transition to nonlinear two-dimensional hydrodynamic turbulence.
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