Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex

Fauconnier, Dieter; Langhe, Chris De; Dick, Erik

doi:10.1016/j.jcp.2009.07.028

Cited by 31 publications

(29 citation statements)

References 38 publications

(139 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equations are solved in Fourier space by a pseudo-spectral method [25] with anisotropic 2/3-de-aliasing for the nonlinear convective terms. Further, a pressurecorrection algorithm is applied in combination with an explicit low-storage six-stage lowdissipation Runge-Kutta method [32].…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…The coherent structure itself, finally breaks down around t = 8. Therefore, it is expected that for t ≥ 9, the flow is fully turbulent and nearly-isotropic [25].…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…The viscous Taylor-Green vortex flow, introduced in 1937 by Taylor et al [23], is considered as a prototype system that describes the production of small-scale eddies due to the mechanism of vortex-line stretching in homogeneous isotropic turbulence [24]. It is one of the simplest environments to study the breakdown process of large-scale vortices into successively smaller ones, and the resulting homogeneous isotropic turbulence [24,25]. In the past decade, the Taylor-Green vortex has become a popular reference case, used in a series of studies on LES methods, e.g., by Fauconnier et al [25], Drikakis et al [26], Chandy and Frankel [27], Johnsen et al [28], Adams [29], and Gassner and Beck [30].…”

Section: Introductionmentioning

confidence: 99%

“…It is one of the simplest environments to study the breakdown process of large-scale vortices into successively smaller ones, and the resulting homogeneous isotropic turbulence [24,25]. In the past decade, the Taylor-Green vortex has become a popular reference case, used in a series of studies on LES methods, e.g., by Fauconnier et al [25], Drikakis et al [26], Chandy and Frankel [27], Johnsen et al [28], Adams [29], and Gassner and Beck [30]. We select the Reynolds number Re = 3000, which is large enough so that natural transition into small-scale homogeneous isotropic decaying turbulence occurs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the performance of relaxation filtering for large-eddy simulation

Fauconnier

Bogey

Dick

2013

Journal of Turbulence

View full text Add to dashboard Cite

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…The coherent structure itself, finally breaks down around t = 8. Therefore, it is expected that for t ≥ 9, the flow is fully turbulent and nearly-isotropic [25].…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the performance of relaxation filtering for large-eddy simulation

Fauconnier

Bogey

Dick

2013

Journal of Turbulence

View full text Add to dashboard Cite

“…The TGV is a well-established computational benchmark to investigate the dissipative and dispersive properties of various numerical schemes, and one can find more details about this research area in conjunction with numerical investigations in [29][30][31][32].…”

Section: Numerical Model and Flow Diagnosticsmentioning

confidence: 99%

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

2017

View full text Add to dashboard Cite

Abstract:The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier-Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor-Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k −4 spectrum at t * = 4, and near the dissipation peak, all methods were capable of predicting the k −5/3 slope accurately when refining the mesh.

show abstract

A high‐order accurate particle‐in‐cell method

Edwards

Bridson

2012

Numerical Meth Engineering

View full text Add to dashboard Cite

We propose the use of high-order accurate interpolation and approximation schemes alongside high-order accurate time integration methods to enable high-order accurate Particle-in-Cell methods. The key insight is to view the unstructured set of particles as the underlying representation of the continuous fields; the grid used to evaluate integro-differential coupling terms is purely auxiliary. We also include a novel regularization term to avoid the accumulation of noise in the particle samples without harming the convergence rate. We include numerical examples for several model problems: advection-diffusion, shallow water, and incompressible Navier-Stokes in vorticity formulation. The implementation demonstrates fourthorder convergence, shows very low numerical dissipation, and is competitive with high-order accurate Eulerian schemes.

show abstract

Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex

Cited by 31 publications

References 38 publications

On the performance of relaxation filtering for large-eddy simulation

On the performance of relaxation filtering for large-eddy simulation

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

A high‐order accurate particle‐in‐cell method

Contact Info

Product

Resources

About