{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,24]],"date-time":"2025-05-24T04:10:29Z","timestamp":1748059829636,"version":"3.41.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100013287","name":"Science Challenge Project","doi-asserted-by":"publisher","award":["TZZT20240303"],"award-info":[{"award-number":["TZZT20240303"]}],"id":[{"id":"10.13039\/501100013287","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013287","name":"Science Challenge Project","doi-asserted-by":"publisher","award":["TZZT20240303"],"award-info":[{"award-number":["TZZT20240303"]}],"id":[{"id":"10.13039\/501100013287","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12472292"],"award-info":[{"award-number":["12472292"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12472292"],"award-info":[{"award-number":["12472292"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s10915-025-02885-2","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T11:47:03Z","timestamp":1744717623000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-Order New Positivity-Preserving MR-WENO Schemes with a Bigger Sufficient CFL Number for Solving Euler Equations"],"prefix":"10.1007","volume":"103","author":[{"given":"Yan","family":"Tan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7440-0195","authenticated-orcid":false,"given":"Jun","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"key":"2885_CR1","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1007\/s10915-015-0147-8","volume":"68","author":"X Cai","year":"2016","unstructured":"Cai, X., Zhang, X., Qiu, J.: Positivity-preserving high order finite volume HWENO schemes for compressible Euler equations. J. Sci. Comput. 68, 464\u2013483 (2016)","journal-title":"J. Sci. Comput."},{"key":"2885_CR2","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The Runge\u2013Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"2885_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111882","volume":"476","author":"S Cui","year":"2023","unstructured":"Cui, S., Ding, S., Wu, K.: Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions? J. Comput. Phys. 476, 111882 (2023)","journal-title":"J. Comput. Phys."},{"key":"2885_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110596","volume":"445","author":"C Fan","year":"2021","unstructured":"Fan, C., Zhang, X., Qiu, J.: Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier\u2013Stokes equations. J. Comput. Phys. 445, 110596 (2021)","journal-title":"J. Comput. Phys."},{"key":"2885_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111446","volume":"467","author":"C Fan","year":"2022","unstructured":"Fan, C., Zhang, X., Qiu, J.: Positivity-preserving high order finite difference WENO schemes for compressible Navier\u2013Stokes equations. J. Comput. Phys. 467, 111446 (2022)","journal-title":"J. Comput. Phys."},{"key":"2885_CR6","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1999.6337","volume":"155","author":"J Gressier","year":"1999","unstructured":"Gressier, J., Villedieu, P., Moschetta, J.-M.: Positivity of flux vector splitting schemes. J. Comput. Phys. 155, 199\u2013220 (1999)","journal-title":"J. Comput. Phys."},{"key":"2885_CR7","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/j.jcp.2014.06.046","volume":"274","author":"Y Guo","year":"2014","unstructured":"Guo, Y., Xiong, T., Shi, Y.: A positivity-preserving high order finite volume compact-WENO scheme for compressible Euler equations. J. Comput. Phys. 274, 505\u2013523 (2014)","journal-title":"J. Comput. Phys."},{"key":"2885_CR8","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.jcp.2013.01.024","volume":"242","author":"XY Hu","year":"2013","unstructured":"Hu, X.Y., Adams, N., Shu, C.-W.: Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. J. Comput. Phys. 242, 169\u2013180 (2013)","journal-title":"J. Comput. Phys."},{"key":"2885_CR9","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/j.jcp.2018.03.004","volume":"373","author":"Y Jiang","year":"2018","unstructured":"Jiang, Y., Liu, H.: Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. J. Comput. Phys. 373, 385\u2013409 (2018)","journal-title":"J. Comput. Phys."},{"key":"2885_CR10","volume-title":"Problems of Point-Blast Theory","author":"VP Korobeinikov","year":"1991","unstructured":"Korobeinikov, V.P.: Problems of Point-Blast Theory. American Institute of Physics, College Park (1991)"},{"key":"2885_CR11","first-page":"2213","volume":"83","author":"C Liang","year":"2013","unstructured":"Liang, C., Xu, Z.: Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws. J. Sci. Comput. 83, 2213\u20132238 (2013)","journal-title":"J. Sci. Comput."},{"key":"2885_CR12","unstructured":"Linde, T., Roe, P.L.: Robust Euler codes. In: 13th Computational Fluid Dynamics Conference, AIAA Paper-97-2098"},{"key":"2885_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113440","volume":"519","author":"C Liu","year":"2024","unstructured":"Liu, C., Buzzard, G., Zhang, X.: An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier\u2013Stokes equations. J. Comput. Phys. 519, 113440 (2024)","journal-title":"J. Comput. Phys."},{"key":"2885_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112496","volume":"493","author":"C Liu","year":"2023","unstructured":"Liu, C., Zhang, X.: A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier\u2013Stokes equations. J. Comput. Phys. 493, 112496 (2023)","journal-title":"J. Comput. Phys."},{"key":"2885_CR15","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.jcp.2011.09.006","volume":"231","author":"B Parent","year":"2012","unstructured":"Parent, B.: Positivity-preserving high-resolution schemes for systems of conservation laws. J. Comput. Phys. 231, 173\u2013189 (2012)","journal-title":"J. Comput. Phys."},{"key":"2885_CR16","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s002110050187","volume":"73","author":"B Perthame","year":"1996","unstructured":"Perthame, B., Shu, C.-W.: On positivity preserving finite volume schemes for Euler equations. Numer. Math. 73, 119\u2013130 (1996)","journal-title":"Numer. Math."},{"key":"2885_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112429","volume":"492","author":"Y Ren","year":"2023","unstructured":"Ren, Y., Wu, K., Qiu, J., Xing, Y.: On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation. J. Comput. Phys. 492, 112429 (2023)","journal-title":"J. Comput. Phys."},{"key":"2885_CR18","volume-title":"Similarity and Dimensional Methods in Mechanics","author":"LI Sedov","year":"1959","unstructured":"Sedov, L.I.: Similarity and Dimensional Methods in Mechanics. Academic Press, New York (1959)"},{"key":"2885_CR19","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","volume":"77","author":"C-W Shu","year":"1988","unstructured":"Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439\u2013471 (1988)","journal-title":"J. Comput. Phys."},{"key":"2885_CR20","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10915-024-02493-6","volume":"99","author":"Y Tan","year":"2024","unstructured":"Tan, Y., Zhang, Q., Zhu, J.: A new positivity-preserving technique for high-order schemes to solve extreme problems of Euler equations on structured meshes. J. Sci. Comput. 99, 27 (2024)","journal-title":"J. Sci. Comput."},{"key":"2885_CR21","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1023\/A:1007593601466","volume":"15","author":"H-Z Tang","year":"2000","unstructured":"Tang, H.-Z., Xu, K.: Positivity-preserving analysis of explicit and implicit Lax-Friedrichs schemes for compressible Euler equations. J. Sci. Comput. 15, 19\u201328 (2000)","journal-title":"J. Sci. Comput."},{"key":"2885_CR22","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/j.apnum.2022.06.006","volume":"181","author":"B-S Wang","year":"2022","unstructured":"Wang, B.-S., Li, P., Gao, Z.: High-order well-balanced and positivity-preserving finite-difference AWENO scheme with hydrostatic reconstruction for shallow water equations. Appl. Numer. Math. 181, 483\u2013502 (2022)","journal-title":"Appl. Numer. Math."},{"key":"2885_CR23","first-page":"201","volume":"3","author":"C Wang","year":"2003","unstructured":"Wang, C., Liu, J.-G.: Positivity property of second-order flux-splitting schemes for the compressible Euler equations. Discret. Contin. Dyn. Syst. Ser. B 3, 201\u2013228 (2003)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"key":"2885_CR24","doi-asserted-by":"publisher","first-page":"2124","DOI":"10.1137\/18M1168017","volume":"56","author":"K Wu","year":"2018","unstructured":"Wu, K.: Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics. SIAM J. Numer. Anal. 56, 2124\u20132147 (2018)","journal-title":"SIAM J. Numer. Anal."},{"key":"2885_CR25","doi-asserted-by":"publisher","first-page":"B1302","DOI":"10.1137\/18M1168042","volume":"40","author":"K Wu","year":"2018","unstructured":"Wu, K., Shu, C.-W.: A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. SIAM J. Sci. Comput. 40, B1302\u2013B1329 (2018)","journal-title":"SIAM J. Sci. Comput."},{"key":"2885_CR26","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1007\/s00211-019-01042-w","volume":"142","author":"K Wu","year":"2019","unstructured":"Wu, K., Shu, C.-W.: Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Numer. Math. 142, 995\u20131047 (2019)","journal-title":"Numer. Math."},{"key":"2885_CR27","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s10915-013-9695-y","volume":"57","author":"Y Xing","year":"2013","unstructured":"Xing, Y., Zhang, X.: Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes. J. Sci. Comput. 57, 19\u201341 (2013)","journal-title":"J. Sci. Comput."},{"key":"2885_CR28","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1016\/j.advwatres.2010.08.005","volume":"33","author":"Y Xing","year":"2010","unstructured":"Xing, Y., Zhang, X., Shu, C.-W.: Positivity preserving high order well balanced discontinuous Galerkin methods for the shallow water equations. Adv. Water Resour. 33, 1476\u20131493 (2010)","journal-title":"Adv. Water Resour."},{"key":"2885_CR29","doi-asserted-by":"publisher","first-page":"1066","DOI":"10.1007\/s10915-015-0118-0","volume":"67","author":"T Xiong","year":"2015","unstructured":"Xiong, T., Qiu, J.-M., Xu, Z.: Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations. J. Sci. Comput. 67, 1066\u20131088 (2015)","journal-title":"J. Sci. Comput."},{"key":"2885_CR30","doi-asserted-by":"publisher","first-page":"2213","DOI":"10.1090\/S0025-5718-2013-02788-3","volume":"83","author":"Z Xu","year":"2014","unstructured":"Xu, Z.: Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem. Math. Comput. 83, 2213\u20132238 (2014)","journal-title":"Math. Comput."},{"key":"2885_CR31","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.jcp.2016.10.002","volume":"328","author":"X Zhang","year":"2017","unstructured":"Zhang, X.: On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier\u2013Stokes equations. J. Comput. Phys. 328, 301\u2013343 (2017)","journal-title":"J. Comput. Phys."},{"key":"2885_CR32","doi-asserted-by":"publisher","first-page":"A627","DOI":"10.1137\/110839230","volume":"34","author":"X Zhang","year":"2012","unstructured":"Zhang, X., Liu, Y.-Y., Shu, C.-W.: Maximum-principle-satisfying high order finite volume WENO schemes for convection-diffusion equations. SIAM J. Sci. Comput. 34, A627\u2013A658 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"2885_CR33","doi-asserted-by":"publisher","first-page":"3091","DOI":"10.1016\/j.jcp.2009.12.030","volume":"229","author":"X Zhang","year":"2010","unstructured":"Zhang, X., Shu, C.-W.: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys. 229, 3091\u20133120 (2010)","journal-title":"J. Comput. Phys."},{"key":"2885_CR34","doi-asserted-by":"publisher","first-page":"8918","DOI":"10.1016\/j.jcp.2010.08.016","volume":"229","author":"X Zhang","year":"2010","unstructured":"Zhang, X., Shu, C.-W.: On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys. 229, 8918\u20138934 (2010)","journal-title":"J. Comput. Phys."},{"key":"2885_CR35","first-page":"2752","volume":"467","author":"X Zhang","year":"2011","unstructured":"Zhang, X., Shu, C.-W.: Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments, Proc. R. Soc. A. Math. Phys. Eng. Sci. 467, 2752\u20132776 (2011)","journal-title":"Math. Phys. Eng. Sci."},{"key":"2885_CR36","doi-asserted-by":"publisher","first-page":"2245","DOI":"10.1016\/j.jcp.2011.11.020","volume":"231","author":"X Zhang","year":"2012","unstructured":"Zhang, X., Shu, C.-W.: Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. J. Comput. Phys. 231, 2245\u20132258 (2012)","journal-title":"J. Comput. Phys."},{"key":"2885_CR37","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.jcp.2012.09.032","volume":"234","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Zhang, X., Shu, C.-W.: Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes. J. Comput. Phys. 234, 295\u2013316 (2013)","journal-title":"J. Comput. Phys."},{"key":"2885_CR38","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1016\/j.jcp.2018.09.003","volume":"375","author":"J Zhu","year":"2018","unstructured":"Zhu, J., Shu, C.-W.: A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. J. Comput. Phys. 375, 659\u2013683 (2018)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02885-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-025-02885-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02885-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T13:18:31Z","timestamp":1748006311000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-025-02885-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,15]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["2885"],"URL":"https:\/\/doi.org\/10.1007\/s10915-025-02885-2","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2025,4,15]]},"assertion":[{"value":"8 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"75"}}