Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method

Flad, David; Beck, Andrea; Munz, Claus‐Dieter

doi:10.1016/j.jcp.2015.11.064

Cited by 62 publications

(33 citation statements)

References 23 publications

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“…discontinuous spectral element methods). This study aligns with various recent works that investigate the suitability of DSEM-based uDNS/iLES, considering aspects of solution quality and numerical stability [17,18,21,25,26,49,53,54] .…”

Section: Resultssupporting

confidence: 81%

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

et al. 2018

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a b s t r a c tThe study focusses on the dispersion and diffusion characteristics of discontinuous spectral element methods -specifically discontinuous Galerkin (DG) -via the spatial eigensolution analysis framework built around a one-dimensional linear problem, namely the linear advection equation. Dispersion and diffusion characteristics are of critical importance when dealing with under-resolved computations, as they affect both the numerical stability of the simulation and the solution accuracy. The spatial eigensolution analysis carried out in this paper complements previous analyses based on the temporal approach, which are more commonly found in the literature. While the latter assumes periodic boundary conditions, the spatial approach assumes inflow/outflow type boundary conditions and is therefore better suited for the investigation of open flows typical of aerodynamic problems, including transitional and fully turbulent flows and aeroacoustics. The influence of spurious/reflected eigenmodes is assessed with regard to the presence of upwind dissipation, naturally present in DG methods. This provides insights into the accuracy and robustness of these schemes for under-resolved computations, including under-resolved direct numerical simulation (uDNS) and implicit large-eddy simulation (iLES). The results estimated from the spatial eigensolution analysis are verified using the one-dimensional linear advection equation and successively by performing two-dimensional compressible Euler simulations that mimic (spatially developing) grid turbulence.

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Section: Resultssupporting

confidence: 81%

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

et al. 2018

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“…We expect that the slowdown due to over‐integration is even less severe on future hardware characterized by an increased Flop/Byte ratio providing enhanced compute resources. Efforts have been made in the past to avoid costly over‐integration, eg, by using filtering . These measures can be expected to cause a loss of accuracy as compared to consistent over‐integration (see, for example, the work of Gassner and Beck), which has to be taken into account when evaluating the overall efficiency of a discretization scheme.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Due to several operators involved in the case of the incompressible flow solver (see Equations (39), (40), (41), and (42)), the efficiency of the implementation (throughput) cannot be expressed as a single number as for the compressible solver. The factor labeled iterations includes not only evaluations of the discretized operators but also preconditioners of different complexity (inverse mass matrix versus geometric multigrid) so that this quantity should be understood as an effective number of operator evaluations per time step (see also the discussion in the work of Fehn et al 12 ).…”

Section: Efficiency Modelmentioning

confidence: 99%

“…Efforts have been made in the past to avoid costly over-integration, eg, by using filtering. 36,39 These measures can be expected to cause a loss of accuracy as compared to consistent over-integration (see, for example, the work of Gassner and Beck 36 ), which has to be taken into account when evaluating the overall efficiency of a discretization scheme. From a practical point of view, a 3∕2-dealiasing strategy is often sufficient (see, for example, the work of Beck et al 3 and Section 5.2) and causes an increase in costs by, at most, a factor of roughly 1.5 for moderately high polynomial degrees according to our results.…”

Section: Impact Of Over-integration On Performancementioning

confidence: 99%

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A matrix‐free high‐order discontinuous Galerkin compressible Navier‐Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Fehn

Wall

Kronbichler

2018

Numerical Methods in Fluids

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Summary Both compressible and incompressible Navier‐Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M ≈0.1, in order to mimic incompressible flows. This strategy is widely used for high‐order discontinuous Galerkin (DG) discretizations of the compressible Navier‐Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high‐performance DG solver for the compressible Navier‐Stokes equations based on a highly efficient matrix‐free implementation that targets modern cache‐based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node‐level performance, and our results suggest that there is great potential for further performance improvements for current state‐of‐the‐art DG implementations of the compressible Navier‐Stokes equations. Secondly, this compressible Navier‐Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix‐free implementation. We discuss algorithmic differences between both solution strategies and present an in‐depth numerical investigation of the performance. The considered benchmark test cases are the three‐dimensional Taylor‐Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall‐bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one.

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“…[21,22,23,24,25,26,27,28]). In the absence of an explicit subgrid-scale model, the philosophy behind ILES is to exploit the dissipation properties of the DG scheme to achieve a stable simulation.…”

Section: Introductionmentioning

confidence: 99%

On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

2018

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We assess the performance of a high-order discontinuous Galerkin (DG) approach to simulate wall-bounded turbulent flows for a range of Reynolds numbers. First, a plane channel flow configuration with turbulent heat transfer at Re τ = 640 is considered. Second, a detached flow configuration is investigated. This configuration represents the flow over periodically arranged hills. Four bulk Reynolds numbers Re b are considered: 2 800, 10 595, 19 000, and 37 000. For Re b = 2 800 direct numerical simulation (DNS) is used. Large-eddy simulations (LES) based on the WALE subgrid-scale model are carried out for the higher Re b . The simulation results are compared to reference data from CFD and experiment. hp-convergence analyses are performed which demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this work that the use of a subgrid modelling approach together with local hp-adaptation could greatly improve the accuracy of the solution without penalising the computational cost of the simulation.

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Simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method

Cited by 62 publications

References 23 publications

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES

A matrix‐free high‐order discontinuous Galerkin compressible Navier‐Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

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