A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence

Martı́n, M. Pino; Taylor, Ellen M.; Wu, Minwei; Weirs, V. Gregory

doi:10.1016/j.jcp.2006.05.009

Cited by 441 publications

(309 citation statements)

References 27 publications

(33 reference statements)

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“…Steger-Warming splitting is used for the inviscous terms and then solved by using the fourth-order bandwidth-optimized weighted essentially non-oscillatory scheme (WENO-SYMBO) of Wu and Martín [11] and Martín et al [19]. Viscous terms are discretized by using the eighth-order central scheme.…”

Section: B Numerical Methods and Simulation Parametersmentioning

confidence: 99%

Numerical Study on Wall Temperature Effects on Shock Wave/Turbulent Boundary-Layer Interaction

Zhu¹,

Yu²,

Tong

et al. 2017

AIAA Journal

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The effect of wall temperature on the size of the separation bubble in the shock wave/turbulent boundary-layer interaction of a 24 deg compression ramp with Mach 2.9 is numerically investigated. The ratios of wall temperature to recovery temperature T w ∕T r are 0.6, 1.14, 1.4, and 2.0, respectively. To validate the simulation, the statistical results with T w ∕T r 1.14 are tested and the results show a good agreement with theoretical and experimental results. It is shown that wall temperature has a remarkable effect on the size of the separation bubble and the size increases significantly with the increase of wall temperature. Through theoretical analysis, combined with numerical results, we get a semitheoretical formula L∕δ ∝ T w ∕T r 0.85 , in which L and δ are the length of the separation bubble and the thickness of upstream boundary layer, respectively. The turbulent kinetic energy budgets are also analyzed based on the numerical data, and results show that turbulence kinetic energy is chiefly produced both in the buffer layer and near the shock wave, and turbulent dissipation is mainly in the center of the separation bubble as well as in the nearwall region. It is also shown that the intrinsic compressibility effect is not significant in all these cases. = separation point δ = upstream boundary-layer thickness μ = viscosity coefficient ρ = density

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Section: B Numerical Methods and Simulation Parametersmentioning

confidence: 99%

Numerical Study on Wall Temperature Effects on Shock Wave/Turbulent Boundary-Layer Interaction

Zhu¹,

Yu²,

Tong

et al. 2017

AIAA Journal

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“…No doubt, WENO [8][9][10] and it's derived schemes are of the most successful ones. Especially, some low dissipative WENO type schemes have been proposed, such as compact-WENO [11,12], WENO-Z [13], WENO-SYMBO [14], TWENO [15], which have been successfully used for multi-scales capture. As Pirozzoli [16] reviewed and suggested that the hybridization of a high-order compact scheme with the WENO scheme is good choice for the DNS and larger eddy simulation (LES) of turbulent compressible flows.…”

Section: Introductionmentioning

confidence: 99%

Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

Liang

2014

Commun. Comput. Phys.

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Abstract. In this paper, direct numerical simulation (DNS) is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma ∞ = 2.25,5,6,8. When Ma ∞ = 8, two cases with the ratio of wall-to-reference temperature T w /T ∞ = 1.9 and 10.03 are considered respectively. The wall temperature approaches recovery temperatures for other cases. The characteristics of compressible turbulent boundary layer (CTBL) affected by freestream Mach number and wall temperature are investigated. It focuses on assessing compressibility effects and the validity of Morkovin's hypothesis through computing and analyzing the mean velocity profile, turbulent intensity, the strong Reynolds analogy (SRA) and possibility density function of dilatation term. The results show that, when the wall temperature approaches recovery temperature, the effects of Mach number on compressibility is insignificant. As a result, the compressibility effect is very weak and the Morkovin's hypothesis is still valid for Mach number even up to 8. However, when Mach number equal to 8, the wall temperature effect on the compressibility is sensitive. In this case, when T w /T ∞ = 1.9, the Morkovin's hypothesis is not fully valid. The validity of classical SRA depends on wall temperature directly. A new modified SRA is proposed to eliminate such negative factor in near wall region. Finally the effects of Mach number and wall temperature on streaks are also studied.

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“…One method is the optimization method [22]. For a nonlinear scheme, no analytical formula of the spectral relations can be obtained.…”

Section: Determination Of  M and  Smentioning

confidence: 99%

Nonlinear spectral-like schemes for hybrid schemes

He¹,

Liang

2014

Sci. China Phys. Mech. Astron.

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In spectral-like resolution-WENO hybrid schemes, if the switch function takes more grid points as discontinuity points, the WENO scheme is often turned on, and the numerical solutions may be too dissipative. Conversely, if the switch function takes less grid points as discontinuity points, the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable. Even if the switch function takes less grid points as discontinuity points, the final hybrid scheme is inclined to be more stable, provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability. Following this idea, we propose nonlinear spectral-like schemes named weighted group velocity control (WGVC) schemes. These schemes show not only high-resolution for short waves but also moderate shock capturing capability. Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities. These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points. The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction. The multi-scales phenomena in such problems requires the numerical method to be high order and high resolution. To be reliable, a DNS of such flows must resolve these various scales, particularly smaller ones with accuracy in both amplitude and phase [2]. Concerning high-order and highresolution schemes, there have been upwind compact schemes [3,4], dispersion-relation preserving schemes [5] and wavenumber-extended finite difference schemes [6]. These schemes are all designed for high resolution of short waves with respect to the computational grid. Another highresolution schemes are explicit/compact central schemes [7] which have no dissipation resulted in providing spurious solutions and leading to inevitable stability problems [8,9].However, these methods above are limited to compute flows without discontinuities. To capture shocks, treating these methods nonlinearly is required [4]. For flows with discontinuities, WENO [10] schemes which have been demonstrated very promising shock-capturing capabilities and high order accuracy are widely used. However, numerical tests also indicate that classical WENO schemes are usually not optimal for computing turbulent flows or aeroacoustic fields because they are too diffusive for short waves [11].

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A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence

Cited by 441 publications

References 27 publications

Numerical Study on Wall Temperature Effects on Shock Wave/Turbulent Boundary-Layer Interaction

Numerical Study on Wall Temperature Effects on Shock Wave/Turbulent Boundary-Layer Interaction

Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

Nonlinear spectral-like schemes for hybrid schemes

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