Robustness of the hybrid DRP‐WENO scheme for shock flow computations

Wan, Zhen-Hua; Zhou, Lin; Sun, Daoyuan

doi:10.1002/fld.2724

Cited by 8 publications

(7 citation statements)

References 25 publications

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“…So, we can say that the dissipative WENO-JS scheme cannot accurately predict the location of triple point and also is unable to capture the waviness of the contact discontinuity in detail. These observations regarding the differences in the performance of the schemes agree with the findings of Wan et al [48]. We also notice that the primary vortex is stretched in the normal direction (y-direction) when using the WENO-JS scheme while the stretching is less for the WENO3P-LIM-5, q = 2, and WENO4P-LIM-5, q = 2, schemes on the coarser grid 1 as seen in Fig.…”

Section: Two-dimensional Viscous Shock Tube Problemsupporting

confidence: 91%

“…Recently, Zhou et al [47] have studied the gridconverged solution of viscous shock tube problem with a high-order gas kinetic scheme. This problem has also been studied as a test case in many articles [7,48,49]. In the present study, we perform computations of the viscous shock tube problem for a Reynolds number Re = 1000 using the WENO-JS, WENO3P-LIM-5, q = 2, and WENO4P-LIM-5, q = 2, schemes.…”

Section: Two-dimensional Viscous Shock Tube Problemmentioning

confidence: 99%

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Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Kumar

Ghosh

2021

Shock Waves

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High-order bandwidth-optimized weighted essentially non-oscillatory (WENO) schemes with limiters are applied in this study to a wide variety of problems. A comparison of the performance of these schemes with three-point and four-point stencils is shown for one-dimensional and two-dimensional test problems. For the one-dimensional and two-dimensional test cases, these schemes show their advantage over the standard fifth-order and the seventh-order WENO schemes proposed in the literature in capturing the small-scale structures appearing in these flows. Effects of the limiter threshold values are discussed for the bandwidth-optimized WENO schemes. Further, the bandwidth-optimized WENO schemes with limiters are compared with other variants of the WENO scheme found in the literature. Direct numerical simulation of supersonic channel flow is also performed with the bandwidth-optimized WENO scheme (with three-point stencil) with limiter, and the results are found to be in good agreement with the literature. This scheme is then used for performing DNS of shock train in a turbulent channel flow. KeywordsDNS • Bandwidth-optimized WENO scheme • Compressible channel flow • Shock train Abbreviations LES Large eddy simulation DNS Direct numerical simulation WENO3P-LIM-'P' Bandwidth-optimized third-order weighted essentially non-oscillatory (WENO) scheme with relative total variation limiter [1,2]. 'P' is the numerical threshold value of limiter. Candidate stencil has three points. Set of candidate stencils is symmetric at the interface. Total number of points used for the flux reconstruction at the interface is 6 WENO4P-LIM-'P' Bandwidth-optimized fourth-order WENO scheme with relative total variation limiter [1,2]. 'P' is the numerical threshold value of limiter. Candidate stencil has four points. Set of candidate Communicated by D. Zeidan.

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Section: Two-dimensional Viscous Shock Tube Problemsupporting

confidence: 91%

Section: Two-dimensional Viscous Shock Tube Problemmentioning

confidence: 99%

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Kumar

Ghosh

2021

Shock Waves

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“…The Re = 200 case has been simulated by many authors (Daru & Tenaud 2001;Sjögreen & Yee 2003;Daru & Tenaud 2004;Kim & Kim 2005a,b;Daru & Tenaud 2009;Houim & Kuo 2011;Wan et al 2012;Sun et al 2014;Kotov et al 2014;Tenaud et al 2015;Wang & Ren 2015;. At this relatively low Reynolds number, the results presented in different papers are quite consistent when the grid is fine enough.…”

Section: The Re = 200 Casementioning

confidence: 83%

Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

Zhou

Liu³

2018

Physics of Fluids

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The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics is of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru & Tenaud (Daru, V. & Tenaud, C. 2001 Evaluation of TVD high resolution schemes for unsteady viscous shocked flows. Computers & Fluids 30, 89-113) proposed a two-dimensional model problem as a numerical test case for highresolution schemes to simulate the flow field in a square closed shock tube. Though many researchers have tried this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting gridconverged solutions for this problem by using a newly-developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analysed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface.

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“…One can also clearly see from Figure 6b that the predicted wave shape remains almost unchanged. The linear advection equation u t þ u x ¼ 0 is also solved under the following initial condition [27][28][29][30]:…”

Section: One-dimensional Verification Studiesmentioning

confidence: 99%

Development of a symplectic and phase error reducing perturbation finite-difference advection scheme

Zhi

Sheu³

2016

Numerical Heat Transfer, Part B: Fundamentals

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The aim of this work is to develop a new scheme for solving the pure advection equation. This scheme formulated within the perturbation finite-difference context not only conserves symplecticity but also preserves the numerical dispersion relation equation. The employed symplectic integrator of secondorder accuracy in time enables calculation of a long-time accurate solution in the sense that the Hamiltonian is conserved at all times. The generalized highorder spatially accurate perturbation difference scheme optimizes numerical phase accuracy through the minimization of the difference between the numerical and exact dispersion relation equations. Our proposed new class of phase error reducing perturbation difference schemes can in addition locally capture discontinuities underlying the concept of applying a shope/flux limiter. The high-order spatial accuracy can be recovered in a smooth region. Besides the Fourier analysis of the discretization errors, anisotropy and dispersion analyses are both conducted on the dispersion-relation and symplecticity-preserving pure advection scheme to shed light on the distinguished nature of the proposed scheme. Numerical tests are carried out and the results compare well with the exact solutions, demonstrating the efficiency, accuracy, and the discontinuity-resolving ability using the proposed class of high-resolution perturbation finite-difference schemes. ARTICLE HISTORY

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Robustness of the hybrid DRP‐WENO scheme for shock flow computations

Cited by 8 publications

References 25 publications

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

Development of a symplectic and phase error reducing perturbation finite-difference advection scheme

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