Very-High-Order WENO Schemes

Gerolymos, G. A.; Senechal, D.; Vallet, I.

doi:10.2514/6.2009-1612

Cited by 50 publications

(101 citation statements)

References 33 publications

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“…More importantly, the mesh (65% of the nodes were stretched near the walls geometrically with ratio r j = 1.0427, the remaining nodes in the outer region being equidistant) was kept fine in the entire nearwall region, with N y + ≤10 = 26 grid cells between the wall and y + 10, and remained fine up to the centerline where the wall-normal cell-size was ∆y + CL 3.1. This spatial resolution, combined with the O(∆ 17 ) scheme used (Gerolymos et al 2009(Gerolymos et al , 2010) is quite fine in view of current state-of-the-art DNS at this Re τw 180 (Vreman & Kuerten 2014a, 2016. Statistics were acquired at high sampling frequency (at every iteration; ∆t Vreman & Kuerten (2016) further substantiate the validity of the computations.…”

Section: ε Ij -Transport Budgetsmentioning

confidence: 95%

“…The solver used to acquire these data was described in Gerolymos, Sénéchal & Vallet (2010) and uses an O(∆ 17 ) upwind-biased discretization for the convective terms (Gerolymos, Sénéchal & Vallet 2009). It has been validated by systematic (Gerolymos et al 2010(Gerolymos et al , 2013 comparison with standard (Moser et al 1999;delÁlamo & Jiménez 2003;Hoyas & Jiménez 2006 DNS data (profiles, 2-point correlations and spectra in the homogeneous xzdirections, and r ij -transport budgets), including assessment of the influence of compressibility at the low-Mach-number limit (Gerolymos et al 2013, Appendix A, pp.…”

Section: Introductionmentioning

confidence: 99%

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The dissipation tensor in wall turbulence

Gerolymos¹,

Vallet²

2016

J. Fluid Mech.

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The paper investigates the dissipation tensor ε ij in wall turbulence. Available DNS data are examined to illustrate the differences in the anisotropy of the dissipation tensor ε ij with respect to the anisotropy of the Reynolds-stresses r ij . The budgets of the transport equations of the dissipation tensor ε ij are studied using novel DNS data of low-Reynoldsnumber turbulent plane channel flow with spatial resolution sufficiently fine to accurately determine the correlations of products of 2-derivatives of fluctuating velocities u i and pressure p which appear in various terms. Finally, the influence of the Reynolds number on the diagonal components of ε ij (ε xx , ε yy , ε zz ) and on the various terms in their transport equations is studied using available DNS data of Vreman and Kuerten (Phys. Fluids 26 (2014) 085103).

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Section: ε Ij -Transport Budgetsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

The dissipation tensor in wall turbulence

Gerolymos¹,

Vallet²

2016

J. Fluid Mech.

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“…1) were run using an O(∆x 17 ) upwind-biased scheme (Gerolymos et al 2009b) for the convective terms and an O(∆x 2 ) conservative centered scheme (Gerolymos et al 2010) for the viscous terms, using explicit dual-time-stepping timeintegration (Gerolymos et al 2009a). Statistics were acquired using an onboard movingaverages technique (Gerolymos et al 2010, §4.4, p. 791).…”

Section: Dns Computationsmentioning

confidence: 99%

Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow

Gerolymos

Vallet

2014

J. Fluid Mech.

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We investigate the fluctuations of thermodynamic state-variables in compressible aerodynamic wall-turbulence, using results of direct numerical simulation (DNS) of compressible turbulent plane channel flow. The basic transport equations governing the behaviour of thermodynamic variables (density, pressure, temperature and entropy) are reviewed and used to derive the exact transport equations for the variances and fluxes (transport by the fluctuating velocity field) of the thermodynamic fluctuations. The scaling with Reynolds and Mach number of compressible turbulent plane channel flow is discussed. Correlation coefficients and higher-order statistics of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables from a well-resolved DNS are analysed. Implications of these results both to the understanding of the thermodynamic interactions in compressible wall-turbulence and to possible improvements in statistical modelling are assessed. Finally, the required extension of existing DNS data to fully characterise this canonical flow is discussed.

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“…Recently, Borges et al [5] suggested to use the whole five-points stencil to devise a smoothness indicator of higher order than the classical smoothness indicator proposed by Jiang and Shu [3] and developed the WENO-Z scheme. On the other hand, a class of WENO schemes higher than the fifth order are designed by Balsara and Shu in [6] and by Gerolymos et al in [7]. Wang and Chen [8] proposed optimized WENO schemes for linear waves with discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Multistep weighted essentially non‐oscillatory scheme

Shen

Liu

Yang

2014

Numerical Methods in Fluids

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SUMMARYA fifth-order accurate multistep weighted essentially non-oscillatory (WENO) scheme is constructed in this paper. Different from the traditional WENO schemes, which are designed to have (2r 1/th order accuracy in the smooth regions directly from r candidate stencils, the new scheme is constructed through (r 1/ weighting steps. In each step, only two neighboring stencils are used to construct the intermediate fluxes (or the final flux), which are only one order higher than the fluxes obtained from the previous step. Henrick's mapping function is used in each step to satisfy the sufficient condition of fifth-order convergence for a fifth-order WENO scheme; hence, the new scheme is fifth-order accurate in smooth regions. The distinctive advantage of the new scheme is that it can improve the accuracy by one order higher than the traditional WENO schemes at transition points (connecting a smooth region and a discontinuity point); and hence, it improves the accuracy in the regions near discontinuities. Numerical examples show that the new scheme is robust and is less dissipative than the traditional fifth-order WENO schemes.

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Very-High-Order WENO Schemes

Cited by 50 publications

References 33 publications

The dissipation tensor in wall turbulence

The dissipation tensor in wall turbulence

Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow

Multistep weighted essentially non‐oscillatory scheme

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