High Order Conservative Differencing for Viscous Terms and the Application to Vortex-Induced Vibration Flows

Shen, Yiqing; Zha, Gecheng; Chen, Xiangying

doi:10.2514/6.2008-4059

Cited by 45 publications

(63 citation statements)

References 38 publications

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“…However, most efforts, including many in the references mentioned above, mainly focus on the inviscid terms to resolve discontinuities and small scale structures. In order to supplement 5th-order WENO scheme with high-order viscous formula, Shen et al [101] developed a 4th-order conservative scheme with the stencil less than that of the WENO scheme. Deng [10] listed some viscous derivative and interpolation formulas for WCNSs.…”

Section: High-order and High Accurate Cfd Methods For Complex Grid Prmentioning

confidence: 99%

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

Deng

Mao

et al. 2012

Commun. comput. phys.

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Abstract. The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods. Despite the rapid development of high-order algorithms in CFD, the applications of high-order and high accurate methods on complex configurations are still limited. One of the main reasons which hinder the widely applications of these methods is the complexity of grids. Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex. In order to implement highorder finite difference schemes on complex multi-block grids, the geometric conservation law and block-interface conditions are discussed. A conservative metric method is applied to calculate the grid derivatives, and a characteristic-based interface condition is employed to fulfil high-order multi-block computing. The fifth-order WCNS-E-5 proposed by Deng [9, 10] is applied to simulate flows with complex grids, including a double-delta wing, a transonic airplane configuration, and a hypersonic X-38 configuration. The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

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Section: High-order and High Accurate Cfd Methods For Complex Grid Prmentioning

confidence: 99%

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

Deng

Mao

et al. 2012

Commun. comput. phys.

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“…Other restrictions on the equations include the constant specific heats and the Sutherland viscosity law. To get rid of the numerical dissipation as far as possible, we use the 5 th order WENO scheme [16] for the inviscid terms combined with 4 th order central differencing [17] for the viscous terms is employed. Second-order accuracy is obtained in the temporal discretization via dual-time stepping with sub-iterative procedure.…”

Section: Methodsmentioning

confidence: 99%

Towards an entropy-based detached-eddy simulation

Zhao

Yan

et al. 2013

Sci. China Phys. Mech. Astron.

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A concept of entropy increment ratio ( s ) is introduced for compressible turbulence simulation through a series of direct numerical simulations (DNS). s represents the dissipation rate per unit mechanical energy with the benefit of independence of freestream Mach numbers. Based on this feature, we construct the shielding function f s to describe the boundary layer region and propose an entropy-based detached-eddy simulation method (SDES). This approach follows the spirit of delayed detached-eddy simulation (DDES) proposed by Spalart et al. in 2005, but it exhibits much better behavior after their performances are compared in the following flows, namely, pure attached flow with thick boundary layer (a supersonic flat-plate flow with high Reynolds number), fully separated flow (the supersonic base flow), and separated-reattached flow (the supersonic cavity-ramp flow). The Reynolds-averaged Navier-Stokes (RANS) resolved region is reliably preserved and the modeled stress depletion (MSD) phenomenon which is inherent in DES and DDES is partly alleviated. Moreover, this new hybrid strategy is simple and general, making it applicable to other models related to the boundary layer predictions. Advances in computer speeds have made it possible to utilize more accurate methods of simulating and modeling turbulent flows. However, grid requirements and time cost typically restrict direct numerical simulation (DNS) and even large eddy simulation (LES) to only low Reynolds numbers. That is, Reynolds-averaged Navier-Stokes (RANS) equations along with a turbulence model seem still to be a powerful tool for engineering aerodynamic analysis nowadays, whereas, traditional RANS approaches do not resolve any turbulent flow structures, but model the effect of turbulence on the mean flow in terms of representative mean turbulence scales. As a result, all spectral effects are lost in the time averaging process. The unsteady variant of this, URANS, although managing to resolve non-stationary mean flows, will produce too much eddy viscosity polluting the predicted fields [1,2]. For many turbulent flows of engineering importance, traditional RANS or URANS modeling may be an awkward approach or may fail to reproduce the relevant flow physics. Hybrid RANS/LES approaches [3] represent a credible alternative improving the description of such flows at a reasonable cost by taking into account most of the flow unsteadiness. The main idea of these methods is to model the turbulent structures in the attached region of the flow and to solve the large length-scale structures elsewhere. One of the most popular RANS/LES methods is the detached-eddy simulation proposed by Spalart et al. in 1997 [4] (termed in the following as DES97), which is based on a modification of the length scale employed by Spalart-Allmaras RANS model (SA) [5]. Since the time it was put forward, DES97 has been applied successfully to numerous engineering flow problems, especially in high-Reynolds number separated

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“…(22) is a central differencing. For example, in this paper, (m, n) = (À2, 1), (r, s) = (À3, 2), and (p, q) = (À2, 2) are used, and they give [45] …”

Section: The 4th-order Schemes For Viscous Terms [45]mentioning

confidence: 99%

“…(23) can be approximated with the accuracy order not lower than 4th order, the Taylor expansion analysis of (22) and (23) will give the following relation [45] 1…”

Section: The 4th-order Schemes For Viscous Terms [45]mentioning

confidence: 99%

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Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Shen

Zha

2012

Computers & Fluids

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a b s t r a c tA low diffusion E-CUSP (LDE) scheme for preconditioned Navier-Stokes equations is developed. The LDE scheme with high-order WENO reconstruction and high order difference scheme for viscous terms is used to simulate several flows at various speed from low speed natural convection to supersonic flows. The unfactored implicit Gauss-Seidel relaxation scheme, in which the preconditioned Roe's matrices are used, is used for time integration. Numerical results are presented to show efficiency, accuracy and robustness of the new preconditioning scheme.

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High Order Conservative Differencing for Viscous Terms and the Application to Vortex-Induced Vibration Flows

Cited by 45 publications

References 38 publications

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

Towards an entropy-based detached-eddy simulation

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

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