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

Bull, Jonathan; Jameson, Antony

doi:10.2514/1.j053766

Cited by 82 publications

(30 citation statements)

References 53 publications

(109 reference statements)

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“…The negative values of ε c occurring for very low α act as a source of energy and although this is strictly a numerical artifact, it interestingly contributes to adjusting the values of resolved viscous dissipation ( Figure 6), especially around the dissipation peak (t ≈ 8.5). Negative ε c values are as well reported in [41] for the FR-DG scheme. Finally, we note that further investigation is incumbent in order to acquire a more profound comprehension of the underlying mechanisms triggered by reducing α and its effects on VMS-LES simulations.…”

Section: Effect Of α-Roesupporting

confidence: 72%

A high-order multiscale approach to turbulence for compact nodal schemes

Navah

Plata

Couaillier

2020

Computer Methods in Applied Mechanics and Engineering

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This article presents a formulation that extends the variational multiscale modelling for compressible large-eddy simulation to a vast family of compact nodal numerical methods represented by the high-order flux reconstruction scheme. The theoretical aspects of the proposed formulation are laid down via rigorous mathematical derivations which clearly expose the underlying assumptions and approximations and provide sufficient details for accurate reproduction of the methodology. The final form is assessed on a Taylor-Green vortex benchmark with Reynolds number of 5000 and compared to filtered direct numerical simulation data. These numerical experiments exhibit the important role of sufficient de-aliasing, appropriate amount of upwinding from Roe's numerical flux and large/small scale partition, in achieving better agreement with reference data, especially on coarse grids, when compared to the baseline implicit large-eddy simulation.

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Section: Effect Of α-Roesupporting

confidence: 72%

A high-order multiscale approach to turbulence for compact nodal schemes

Navah

Plata

Couaillier

2020

Computer Methods in Applied Mechanics and Engineering

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“…The flow is benchmark cases for evaluating the vortex stretching and dissipation characteristics of numerical schemes by studying the production and break-down of turbulence structures. It has been widely employed by many authors to assess the behaviour of various numerical schemes [13,[65][66][67][68][69][70], in the context of Implicit Large Eddy Simulation (ILES) and how the numerical schemes themselves can possess characteristics that can potentially act as a Sub-Grid Scale (SGS) model. The DNS results of Brachet et.…”

Section: D Taylor-green Vortexmentioning

confidence: 99%

Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

Simmonds

Tsoutsanis

Antoniadis

et al. 2018

Applied Mathematics and Computation

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The paper presents a low-Mach number (LM) treatment technique for high-order, Finite-Volume (FV) schemes for the Euler and the compressible Navier-Stokes equations. We concentrate our efforts on the implementation of the LM treatment for the unstructured mesh framework, both in two and three spatial dimensions, and highlight the key differences compared with the method for structured grids. The main scope of the LM technique is to at least maintain the accuracy of low speed regions without introducing artefacts and hampering the global solution and stability of the numerical scheme. Two families of spatial schemes are considered within the k-exact FV framework: the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO). The simulations are advanced in time with an explicit third-order Strong Stability Preserving (SSP) Runge-Kutta method. Several flow problems are considered for inviscid and turbulent flows where the obtained solutions are compared with referenced data. The associated benefits of the method are analysed in terms of overall accuracy, dissipation characteristics, order of scheme, spatial resolution and grid composition.

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“…As can be seen on Figure 5, the two solutions are in good agreement, especially until T ≈ 9, when the peak of energy dissipation is reached. A discrepancy between the two results is then observed during the flow mixing stage, showing a slightly more antidiffusive behavior provided by the present vortex method compared to the finite difference method of [24] reported here or the spectral methods evoqued in [17,25].…”

Section: Validationmentioning

confidence: 51%

A Semi-Lagrangian Vortex Penalization Method for 3D Incompressible Flows

sci¹

2019

JMS

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A remeshed Vortex method is proposed in this work to simulate threedimensional incompressible flows. The convection equation is solved on particles, using a Vortex method, which are then remeshed on a Cartesian underlying grid. The other differential operators involved in the governing incompressible Navier-Stokes equations are discretized on the grid, through finite differences method or in spectral space. In the present work, the redistribution of the particles on the Cartesian mesh is performed using a directional splitting, allowing to save significant computational efforts especially in the case of 3D flows. A coupling of this semi-Lagrangian method with an immersed boundary method, namely the Brinkman penalization technique, is proposed in this paper in order to efficiently take into account the presence of solid and porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methods and the flexibility of penalization method, is validated and exploited in the context of different flow physics.

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

Cited by 82 publications

References 53 publications

A high-order multiscale approach to turbulence for compact nodal schemes

A high-order multiscale approach to turbulence for compact nodal schemes

Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

A Semi-Lagrangian Vortex Penalization Method for 3D Incompressible Flows

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