Spectral element filtering techniques for large eddy simulation with dynamic estimation

Abstract

Spectral element methods have previously been successfully applied to direct numerical simulation of turbulent flows with moderate geometrical complexity and low to moderate Reynolds numbers. A natural extension of application is to large eddy simulation of turbulent flows, although there has been little published work in this area. One of the obstacles to such application is the ability to deal successfully with turbulence modelling in the presence of solid walls in arbitrary locations. An appropriate tool with which to tackle the problem is dynamic estimation of turbulence model parameters, but while this has been successfully applied to simulation of turbulent wall-bounded flows, typically in the context of spectral and finite volume methods, there have been no published applications with spectral element methods. Here, we describe approaches based on element-level spectral filtering, couple these with the dynamic procedure, and apply the techniques to large eddy simulation of a prototype wall-bounded turbulent flow, the plane channel, using a mixing length-based eddy viscosity subgrid-scale model. The methods outlined here may be carried over without modification to more complex geometries.

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…It was shown by Allaneau and Jameson [32] that setting c > 0 in the ESFR schemes corresponds to damping of the highest-order polynomial mode by the application of a filter to the residual. In fact, filtering is a commonly used stabilization technique with nDG schemes [7,21,46]. Therefore, the FR formulation implicitly includes a stabilization mechanism.…”

“…A stabilization technique developed specifically for high-order methods is to F o r P e e r R e v i e w apply a low-pass filter to the polynomial basis in order to reduce or remove destabilizing high wavenumber components [9,20,21]. An equivalent approach is to include a high-order derivative term, for example the spectral vanishing viscosity (SVV) method [22,23].…”

Spectral-based simulations of particle-laden turbulent flows

“…Spectral filtering can be constructed using either discrete polynomial transform (DPT) or interpolant-projection (see [23]) over each element. DPT filtering can be conveniently applied for methods with modal basis.…”

“…However, there have been limited attempts to apply these methods towards LES. Spectral element filtering strategies have been studied in [99,100,23,101,102]. We have recently developed LES methodologies for compressible flows using two discontinuous spectral element methods [24,25].…”

“…Single-phase large-eddy simulations of channel flow using spectral element method have been performed by Blackburn and Schmidt [23] and more recently by the authors [25]. In [25], flow at two different Reynolds numbers, Re τ = 180 and Re τ = 570 were investigated.…”