A general framework for the evaluation of shock-capturing schemes

Zhao, Guoyan; Sun, Mingbo; Memmolo, Antonio; Pirozzoli, Sergio

doi:10.1016/j.jcp.2018.10.013

Cited by 35 publications

(25 citation statements)

References 20 publications

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“…TVD schemes are oscillation-free in one-dimensional simulations, and thus we would like to use the minmod (MM) limiter and superbee (SB) limiter, which are respectively the most and least restrictive second-order TVD schemes [11], as the baseline schemes to show the different behaviours of high-order schemes. ENO/WENO schemes, however, can not guarantee providing oscillation-free shock-capturing results, and Zhao et al [8] proved that the amplitude of the oscillation relates to the frequency of the smooth disturbance interacting with the discontinuity. Zhao et al [8] also indicated that the activation of linearly unstable stencils might contribute to the resulting exaggerated amplitude or overshoot of propagating smooth waves near the discontinuity.…”

Section: Shock-capturing Schemesmentioning

confidence: 99%

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On the numerical overshoots of shock‐capturing schemes

Zhang

2021

Numerical Methods in Fluids

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This note introduces a simple metric for benchmarking shock-capturing schemes, and this metric is especially focusing on the shock-capturing overshoots, which may damage the robustness of numerical simulations, as well as the reliability of numerical results. The idea is to numerically solve the linear advection equation with square waves of different wavenumbers as initial solutions. Therefore, the exact overshoots after one step of temporal evolution can be easily calculated, and shown as a function of CFL number and reduced wavenumber. The present metric is able to quantify the numerical overshoots of shock-capturing schemes, and some new features of several canonical schemes are shown.

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Section: Shock-capturing Schemesmentioning

confidence: 99%

“…Moreover, we are interested in the behaviour of simulating multiple closely located shock waves, which was not given in Ref. [8]. Another fundamental property needs to be justified is the relative magnitude of the overshoots produced by the shock-capturing schemes at discontinuities.…”

Section: Introductionmentioning

confidence: 99%

On the numerical overshoots of shock‐capturing schemes

Zhang

2021

Numerical Methods in Fluids

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“…The previous subsection provides the results showing the performance of resolving smooth waves. Here, the shock-capturing error analysis method 21 is implemented to examine the performance of capturing discontinuous solutions. In this scalar model problem, sinusoidal disturbances linearly propagate from the left to the right, and in the middle of the scalar field there is an abrupt change of the speed of sound, causing a fixed discontinuity.…”

Section: Shock-capturing Errormentioning

confidence: 99%

“…Zhao et al 21 proposed a standard metric to evaluate the overall performance of high-order finite difference schemes, with taking the computational efficiency into account. Since the seventh-order WENO scheme requires almost 50% more CPU time than the fifth-order WENO scheme 21 while approximating the numerical flux at a given grid point, higher-order schemes may need similar CPU time as that of the fifth-order scheme, for achieving moderate numerical error on (relatively) coarser meshes. Of course, if high accuracy is expected on fine meshes, higher-order schemes still are the more suitable choice since they converge faster than lower-order schemes.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary high‐order extended essentially non‐oscillatory schemes for hyperbolic conservation laws

Zhang

Dong

et al. 2021

Numerical Methods in Fluids

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Achieving high numerical resolution in smooth regions and robustness near discontinuities within a unified framework is the major concern while developing numerical schemes solving hyperbolic conservation laws, for which the essentially non-oscillatory (ENO) type scheme is a favorable solution. Therefore, an arbitrary-high-order ENO-type framework is designed in this article. With using a typical five-point smoothness measurement as the shock-detector, the present schemes are able to detect discontinuities before spatial reconstructions, and thus more spatial information can be exploited to construct incremental-width stencils without crossing discontinuities, ensuring ENO property and high-order accuracy at the same time. The present shock-detection procedure is specifically examined for justifying its performance of resolving high-frequency waves, and a standard metric for discontinuous solutions is also applied for measuring the shock-capturing error of the present schemes, especially regarding the amplitude error in post-shock regions. In general, the present schemes provide high-resolution, and more importantly, the schemes are more efficient compared with the typical WENO schemes since only a five-point smoothness measurement is applied for arbitrary-high-order schemes. Numerical results of canonical test cases also provide evidences of the overall performance of the present schemes.

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“…The reconstruction scheme of Suresh and Huynh has been tested against the classical weighted essentially non-oscillatory (WENO5) scheme by Scandaliato and Liou (2012), where it proved to be more efficient and more accurate. Both of the reconstruction schemes have also been tested in a publication by Zhao et al (2019) addressing the wave propagation errors of smooth waves, when interacting with discontinuities, where the MP5 scheme turned out to be a good compromise regarding wave propagation errors and was slightly more efficient than other schemes with a formal accuracy of 5th order. Further publications have dealt with the properties and defects of shock-capturing schemes.…”

Section: Codementioning

confidence: 99%

Numerical Investigation of Remote Ignition in Shock Tubes

Lipkowicz

Nativel

Cooper

et al. 2020

Flow Turbulence Combust

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Highly resolved two- and three-dimensional computational fluid dynamics (CFD) simulations are presented for shock-tube experiments containing hydrogen/oxygen (H2/O2) mixtures, to investigate mechanisms leading to remote ignition. The results of the reactive cases are compared against experimental results from Meyer and Oppenheim (Proc Combust Inst 13(1): 1153–1164, 1971. 10.1016/s0082-0784(71)80112-1) and Hanson et al. (Combust Flame 160(9): 1550–1558, 2013. 10.1016/j.combustflame.2013.03.026). The results of the non-reactive case are compared against shock tube experiments, recently carried out in Duisburg and Texas. The computational domain covers the end-wall region of the shock tube and applies high order numerics featuring an all-speed approximate Riemann scheme, combined with a 5th order interpolation scheme. Direct chemistry is employed using detailed reaction mechanisms with 11 species and up to 40 reactions, on a grid with up to 2.2 billion cells. Additional two-dimensional simulations are performed for non-reactive conditions to validate the treatment of boundary-layer effects at the inlet of the computational domain. The computational domain covers a region at the end part of the shock tube. The ignition process is analyzed by fields of localized, expected ignition times. Instantaneous fields of temperature, pressure, entropy, and dissipation rate are presented to explain the flow dynamics, specifically in the case of a bifurcated reflected shock. In all cases regions with locally increased temperatures were observed, reducing the local ignition-delay time in areas away from the end wall significantly, thus compensating for the late compression by the reflected shock and therefore leading for first ignition at a remote location, i.e., away from the end wall where the ignition would occur under ideal conditions. In cases without a bifurcated reflected shock, the temperature increase results from shock attenuation. In cases with a bifurcated reflected shock, the formation of a second normal shock and shear near the slip line is found to be crucial for the remote ignition to take place. Overall, the two- and three-dimensional simulations were found to qualitatively explain the occurrence of remote ignition and to be quantitatively correct, implying that they include the correct physics.

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A general framework for the evaluation of shock-capturing schemes

Cited by 35 publications

References 20 publications

On the numerical overshoots of shock‐capturing schemes

On the numerical overshoots of shock‐capturing schemes

Arbitrary high‐order extended essentially non‐oscillatory schemes for hyperbolic conservation laws

Numerical Investigation of Remote Ignition in Shock Tubes

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