A simple extended compact nonlinear scheme with adaptive dissipation control

Zhang, Huaibao; Zhang, Fan; Li, Jun; McDonough, J. M.; Xu, Chunguang

doi:10.1016/j.cnsns.2020.105191

Cited by 19 publications

(7 citation statements)

References 39 publications

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“…Numerical simulations of compressible flows are a highly challenging topic because shock waves which cause strong density, velocity and pressure discontinuities, need to be tackled by using robust [1], accurate [2,3] and efficient [4,5] shock-capturing schemes, the development of which is still not trivial. This topic becomes especially challenging while high numerical resolution and computational robustness are expected to be provided by a unified framework of numerical schemes, since achieving high-resolution usually expects high-order polynomials for spatial approximation, and high-order polynomials tend to be oscillatory if they are crossing discontinuities (Gibbs phenomenon).…”

Section: Introductionmentioning

confidence: 99%

“…Numerical simulations of compressible flows are a highly challenging topic since shock waves, which cause strong density, velocity, and pressure discontinuities, need to be tackled by using robust, 1 accurate, 2,3 and efficient 4,5 shock-capturing schemes, the development of which, however, is still not trivial. This topic becomes even more challenging when it comes to high-order shock-capturing schemes, since for which, the satisfaction of high numerical resolution and strong computational robustness are contradictory.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the numerical overshoots of shock‐capturing schemes

Zhang

2021

Numerical Methods in Fluids

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“…22 In general, no doubt, further improving the efficiency of these nonlinear shock-capturing schemes is a crucial issue. [23][24][25] Therefore, an idea first sketched in Reference 26 and extended by Zhang et al 27 is further developed and analyzed in this work, in order to reduce the overall computational effort of high-resolution solutions.…”

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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“…In Computational Fluid Dynamics(CFD), numerical dissipation is considered to derive from the truncation error introduced by the discrete convection term of the spatial discrete schemes, which is closely related to the computational accuracy and stability of the scheme. CFD researchers often use the method of reducing numerical dissipation to construct higher precision computational schemes [1][2][3]. The spatial discrete scheme consists of two parts, the difference scheme and the flux splitting scheme, and this paper mainly discusses the numerical dissipation characteristics of the flux splitting scheme, while the upwind scheme, as the mainstream scheme for solving convective fluxes in CFD at present [4], becomes the object of study in this paper.…”

Section: Introductionmentioning

confidence: 99%

Numerical dissipation of flux splitting schemes for contact discontinuities

Liu

Fang

Wei

2021

Preprint

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The contact discontinuity is simulated by three kinds of flux splitting schemes to evaluate and analyse the influence of numerical dissipation in this paper. The numerical results of one-dimensional contact discontinuity problem show that if the flow velocity on both sides of the contact discontinuity is not simultaneously supersonic, the non-physical pressure and velocity waves may occur when the initial theoretically contact discontinuity is smeared into a transition zone spanning several grid-cells caused by numerical dissipations. Since these non-physical waves have no effect on the corresponding density dissipation, this paper considers these fluctuations as only numerical errors and are not part of the numerical dissipation. In addition, for two-dimensional flow field, the characteristics of high-order accuracy difference schemes, i.e. low dissipation and high resolution, may induce the multi-dimensional non-physical waves that interfere with each other to produce more complex non-physical flow structures, so the fluctuations in the calculated results should be treated with caution.

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A simple extended compact nonlinear scheme with adaptive dissipation control

Cited by 19 publications

References 39 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 dissipation of flux splitting schemes for contact discontinuities

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