{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T07:20:05Z","timestamp":1780644005486,"version":"3.54.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2006,9,26]],"date-time":"2006-09-26T00:00:00Z","timestamp":1159228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2006,9,26]],"date-time":"2006-09-26T00:00:00Z","timestamp":1159228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2007,5]]},"DOI":"10.1007\/s10915-006-9111-y","type":"journal-article","created":{"date-parts":[[2006,9,25]],"date-time":"2006-09-25T15:15:28Z","timestamp":1159197328000},"page":"273-305","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":98,"title":["A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions"],"prefix":"10.1007","volume":"31","author":[{"given":"Shuhai","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2006,9,26]]},"reference":[{"key":"9111_CR1","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1137\/S003614450036757X","volume":"43","author":"S. Gottlieb","year":"2001","unstructured":"Gottlieb S., Shu C.-W., Tadmor E. (2001). Strong stability preserving high order time discretization methods. SIAM Rev. 43:89\u2013112","journal-title":"SIAM Rev."},{"key":"9111_CR2","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0021-9991(83)90136-5","volume":"49","author":"A. Harten","year":"1983","unstructured":"Harten A. (1983). High-resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:357\u2013393","journal-title":"J. Comput. Phys."},{"key":"9111_CR3","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0021-9991(87)90031-3","volume":"71","author":"A. Harten","year":"1987","unstructured":"Harten A., Engquist B., Osher S., Chakravarthy S. (1987). Uniformly high order essentially non-oscillatory schemes, III. J. Comput. Phys. 71:231\u2013303","journal-title":"J. Comput. Phys."},{"key":"9111_CR4","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.jcp.2005.01.023","volume":"207","author":"A.K. Henrick","year":"2005","unstructured":"Henrick A.K., Aslam T.D., Powers J.M. (2005). Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207:542\u2013567","journal-title":"J. Comput. Phys."},{"key":"9111_CR5","doi-asserted-by":"crossref","unstructured":"Jameson A. (1993). Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows. AIAA Paper 93\u20133359","DOI":"10.2514\/6.1993-3359"},{"key":"9111_CR6","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/S0376-0421(01)00004-5","volume":"37","author":"A. Jameson","year":"2001","unstructured":"Jameson A. (2001). A perspective on computational algorithms for aerodynamic analysis and design. Prog. Aerosp. Sci. 37:197\u2013243","journal-title":"Prog. Aerosp. Sci."},{"key":"9111_CR7","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"G.-S. Jiang","year":"1996","unstructured":"Jiang G.-S., Shu C.-W. (1996). Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126:202\u2013228","journal-title":"J. Comput. Phys."},{"key":"9111_CR8","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1006\/jcph.1999.6207","volume":"150","author":"G.-S. Jiang","year":"1999","unstructured":"Jiang G.-S., Wu C.-C. (1999). A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 150:561\u2013594","journal-title":"J. Comput. Phys."},{"key":"9111_CR9","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1006\/jcph.1994.1187","volume":"115","author":"X.-D. Liu","year":"1994","unstructured":"Liu X.-D., Osher S., Chan T. (1994), Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115:200\u2013212","journal-title":"J. Comput. Phys."},{"key":"9111_CR10","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1137\/0721060","volume":"21","author":"S. Osher","year":"1984","unstructured":"Osher S., Chakravarthy C. (1984). High-resolution schemes and the entropy condition. SIAM J. Numer. Anal. 21:955\u2013984","journal-title":"SIAM J. Numer. Anal."},{"key":"9111_CR11","volume-title":"Compressible Fluid Flow","author":"M.A. Saad","year":"1993","unstructured":"Saad M.A. (1993). Compressible Fluid Flow. Prentice Hall, Englewood Cliffs, NJ"},{"key":"9111_CR12","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1016\/j.jcp.2003.09.017","volume":"194","author":"S. Serna","year":"2004","unstructured":"Serna S., Marquina A. (2004). Power ENO methods: a fifth-order accurate weighted power ENO method. J. Comput. Phys. 194:632\u2013658","journal-title":"J. Comput. Phys."},{"key":"9111_CR13","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1016\/S0021-9991(03)00094-9","volume":"186","author":"J. Shi","year":"2003","unstructured":"Shi J., Zhang Y.-T., Shu C.-W. (2003). Resolution of high-order WENO schemes for complicated flow structures. J. Comput. Phys. 186:690\u2013696","journal-title":"J. Comput. Phys."},{"key":"9111_CR14","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/0909073","volume":"9","author":"C.-W. Shu","year":"1988","unstructured":"Shu C.-W. (1988). Total-Variation-Diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9:1073\u20131084","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9111_CR15","doi-asserted-by":"crossref","unstructured":"Shu, C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Lecture Notes in Mathematics, Vol. 1697. Springer, Berlin, pp. 325\u2013432.","DOI":"10.1007\/BFb0096355"},{"key":"9111_CR16","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. (1988). Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77:439\u2013471","journal-title":"J. Comput. Phys."},{"key":"9111_CR17","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/0021-9991(89)90222-2","volume":"83","author":"C.-W. Shu","year":"1989","unstructured":"Shu C.-W., Osher S. (1989). Efficient implementation of essentially non- oscillatory shock capturing schemes II. J. Comput. Phys. 83:32\u201378","journal-title":"J. Comput. Phys."},{"key":"9111_CR18","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0021-9991(79)90145-1","volume":"32","author":"B. Van Leer","year":"1979","unstructured":"Van Leer B. (1979). Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov\u2019s method. J. Comput. Phys. 32:101\u2013136","journal-title":"J. Comput. Phys."},{"key":"9111_CR19","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1006\/jcph.1995.1084","volume":"118","author":"V. Venkatakrishnan","year":"1995","unstructured":"Venkatakrishnan V. (1995). Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 118:120\u2013130","journal-title":"J. Comput. Phys."},{"key":"9111_CR20","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0021-9991(84)90142-6","volume":"54","author":"P. Woodward","year":"1984","unstructured":"Woodward P., Colella P. (1984). The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54:115\u2013173","journal-title":"J. Comput. Phys."},{"key":"9111_CR21","doi-asserted-by":"crossref","first-page":"116101","DOI":"10.1063\/1.2084233","volume":"17","author":"S. Zhang","year":"2005","unstructured":"Zhang, S., Zhang, Y.-T., and Shu, C.-W. (2005). Multistage interaction of a shock wave and a strong vortex. Phys. Fluid\n                           17, 116101.","journal-title":"Phys. Fluid"},{"key":"9111_CR22","doi-asserted-by":"crossref","first-page":"046709","DOI":"10.1103\/PhysRevE.68.046709","volume":"68","author":"Y.-T. Zhang","year":"2003","unstructured":"Zhang Y.-T., Shi J., Shu C.-W., Zhou Y. (2003). Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers. Phys. Rev. E\n                           68, 046709","journal-title":"Phys. Rev. E"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-006-9111-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-006-9111-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-006-9111-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-006-9111-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T19:38:26Z","timestamp":1652816306000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-006-9111-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9,26]]},"references-count":22,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2007,5]]}},"alternative-id":["9111"],"URL":"https:\/\/doi.org\/10.1007\/s10915-006-9111-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,9,26]]},"assertion":[{"value":"26 September 2006","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}