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    "title": "Jiang–Shu WENO: accurate smooth waves and sharp changes",
    "summary": "Jiang and Shu develop derivative-based smoothness indicators and efficient finite-difference WENO implementations that recover fifth-order spatial accuracy in regular smooth regions while reducing the contribution of stencils crossing discontinuities.\n\nSimulating waves and flows poses a difficult tradeoff: accurate formulas for smooth waves can produce artificial ringing near abrupt changes. Earlier ENO methods select a smooth local stencil; Liu, Osher and Chan introduced weighted combinations of candidate stencils. Guang-Shan Jiang and Chi-Wang Shu improve this approach with smoothness measurements based on derivatives of reconstruction polynomials. The measurements guide a blend that approaches accurate linear weights where the data are smooth and suppresses unsuitable stencils near discontinuities. Their paper also develops computational shortcuts and compares implementations on contemporary computers. The contribution is an influential improvement within the WENO family, rather than the invention of all WENO methods. Its familiar fifth-order label concerns spatial accuracy under suitable conditions. Later analysis finds order loss near certain smooth critical points and shows that the small regularization parameter matters. Shock tests, smooth-solution convergence and hardware-specific speedups are distinct kinds of evidence.",
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        "description": "The high-order finite-difference reconstruction uses its stencil, smoothness indicators, nonlinear weights and flux/time discretization assumptions. Formal order in smooth regions differs from behavior near critical points or discontinuities. It is not a universal nonoscillation, convergence or optimal-performance guarantee for every conservation law. Later WENO repairs and variants remain separate.",
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      "statement": "# Jiang–Shu WENO: accurate smooth waves and sharp changes\n\nJiang and Shu develop derivative-based smoothness indicators and efficient finite-difference WENO implementations that recover fifth-order spatial accuracy in regular smooth regions while reducing the contribution of stencils crossing discontinuities.\n\nSimulating waves and flows poses a difficult tradeoff: accurate formulas for smooth waves can produce artificial ringing near abrupt changes. Earlier ENO methods select a smooth local stencil; Liu, Osher and Chan introduced weighted combinations of candidate stencils. Guang-Shan Jiang and Chi-Wang Shu improve this approach with smoothness measurements based on derivatives of reconstruction polynomials. The measurements guide a blend that approaches accurate linear weights where the data are smooth and suppresses unsuitable stencils near discontinuities. Their paper also develops computational shortcuts and compares implementations on contemporary computers. The contribution is an influential improvement within the WENO family, rather than the invention of all WENO methods. Its familiar fifth-order label concerns spatial accuracy under suitable conditions. Later analysis finds order loss near certain smooth critical points and shows that the small regularization parameter matters. Shock tests, smooth-solution convergence and hardware-specific speedups are distinct kinds of evidence.\n\n## Scientific scope\n\nThe high-order finite-difference reconstruction uses its stencil, smoothness indicators, nonlinear weights and flux/time discretization assumptions. Formal order in smooth regions differs from behavior near critical points or discontinuities. It is not a universal nonoscillation, convergence or optimal-performance guarantee for every conservation law. Later WENO repairs and variants remain separate.\n\n## People and systems\n\nGuang-Shan Jiang; Chi-Wang Shu\n\n\n\n## Original sources\n\n- [Jiang and Shu1996: Efficient Implementation of Weighted ENO Schemes](https://lsec.cc.ac.cn/lcfd/DEWENO/paper/WENO_1996.pdf)\n- [Henrick, Aslam and Powers2005: Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points](https://academicweb.nd.edu/~powers/paper.list/jcp.weno5m.05.pdf)\n",
      "summary": "Jiang and Shu develop derivative-based smoothness indicators and efficient finite-difference WENO implementations that recover fifth-order spatial accuracy in regular smooth regions while reducing the contribution of stencils crossing discontinuities.\n\nSimulating waves and flows poses a difficult tradeoff: accurate formulas for smooth waves can produce artificial ringing near abrupt changes. Earlier ENO methods select a smooth local stencil; Liu, Osher and Chan introduced weighted combinations of candidate stencils. Guang-Shan Jiang and Chi-Wang Shu improve this approach with smoothness measurements based on derivatives of reconstruction polynomials. The measurements guide a blend that approaches accurate linear weights where the data are smooth and suppresses unsuitable stencils near discontinuities. Their paper also develops computational shortcuts and compares implementations on contemporary computers. The contribution is an influential improvement within the WENO family, rather than the invention of all WENO methods. Its familiar fifth-order label concerns spatial accuracy under suitable conditions. Later analysis finds order loss near certain smooth critical points and shows that the small regularization parameter matters. Shock tests, smooth-solution convergence and hardware-specific speedups are distinct kinds of evidence.",
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    "title": "Jiang–Shu WENO: accurate smooth waves and sharp changes",
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