DSMC data-improved numerical simulation of hypersonic flow past a flat plate in near-continuum regime

Ou, Jihui; Chen, Jie

doi:10.1016/j.compfluid.2019.104308

Cited by 12 publications

(3 citation statements)

References 41 publications

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“…Distribution characteristics and mixing mechanisms of a liquid jet injected into a cavity-based supersonic combustor were studied in . Numerical simulation of hypersonic flow past a flat plate in near-continuum regime was performed in Ou and Chen (2019). Turbulent premixed flame kernels in supersonic flows were studied in Ochs, Ranjan, Ranjan and Menon (2019).…”

Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

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Section: Applicationsmentioning

confidence: 99%

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Shu¹

2020

Acta Numerica

118

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“…Shi 等 [71] 研究了粗糙元对高超声速边界层感受性的影响. Li 等 [42] 研究了液体射流在凹腔超声速燃烧室中的分布特性和混合机理. Ou 和 Chen [57] 对高超声速近连续区平板绕流进行了数值模拟. 除了以上介绍的一些应用以外, WENO-JS 格式 [32,73] 在多相多物质流、爆轰、燃烧和火焰, 辐射传输和动理学方程, 流体结构与弹性分析等领域也有着重要的应用.…”

Section: 这些候选模板上多项式的任意凸组合理论上只有三阶精度为了在解的光滑区域获得更高的数值精度选定包含所有候选模板中网格的大模板unclassified

Development and prospect of high-order WENO schemes

Jun,

Chi-Wang,

Jianxian

2023

Sci. Sin.-Math.

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朱君等: 高精度 WENO 格式的发展与展望荡并破坏数值格式的稳定性. 著名的 Godunov 定理指出只有非线性格式才能在解的光滑区域实现高阶数值精度并能在解的非光滑区域较好地模拟强间断 (参见文献 [22, 23]). 以全局总变差减少 (total variation diminishing, TVD) 格式为代表的非线性格式 [26,55] 可以较好地解决这个问题. TVD 格式一般是通过设计如最小模数 (minmod) 限制器 [26] 来实现非线性格式的有效构造 (参见文献 [38]), 能够对解的不连续区域产生单调的变换并在连续和单调区域中获得高阶数值精度 (参见文献 [56]).

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“…Jiang and Shu [7] extended the idea to the FDM and proposed the efficient implementation of WENO schemes, which greatly succeeded in high-order accuracy and high efficiency. Until now, the ENO and WENO schemes have been applied in many physical areas, such as turbulent flows [8], supersonic and hypersonic flows [9], astrophysical flows, atmospherical and climate sciences [10], and computational biology [11].…”

Section: Introductionmentioning

confidence: 99%

Stability and Resolution Analysis of the Wavelet Collocation Upwind Schemes for Hyperbolic Conservation Laws

Yang¹,

Wang²,

Liu³

et al. 2023

Preprint

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A system of wavelet collocation upwind schemes is constructed for solving hyperbolic conserva-tion laws based on a class of interpolation wavelets. The bias magnitude and symmetry factor are defined to depict the asymmetry of the adopted scaling basis function in wavelet theory. Effects of characteristics of the scaling functions on the schemes are explored based on numerical tests and Fourier analysis. The numerical results reveal that the stability of the constructed scheme is af-fected by the smoothness order, N, and the asymmetry of the scaling function. The dissipation analysis suggests that schemes with Neven have negative dissipation coefficients, leading to unstable behaviors. Only scaling functions with Nodd and bias magnitude of 1 can be used to construct stable upwind schemes due to the non-negative dissipation coefficients. Resolution of the wavelet scheme tends to the spectral resolution as the order of accuracy of the scheme in-creases.

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DSMC data-improved numerical simulation of hypersonic flow past a flat plate in near-continuum regime

Cited by 12 publications

References 41 publications

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Development and prospect of high-order WENO schemes

Stability and Resolution Analysis of the Wavelet Collocation Upwind Schemes for Hyperbolic Conservation Laws

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