{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T21:57:00Z","timestamp":1780351020106,"version":"3.54.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,2,16]],"date-time":"2017-02-16T00:00:00Z","timestamp":1487203200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Natural Science Foundation of China (CN)","award":["11302250"],"award-info":[{"award-number":["11302250"]}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2015JQ1008"],"award-info":[{"award-number":["2015JQ1008"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004750","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["201514U8005"],"award-info":[{"award-number":["201514U8005"]}],"id":[{"id":"10.13039\/501100004750","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science Foundation for Post-doctoral Scientist of China","award":["2015M570084"],"award-info":[{"award-number":["2015M570084"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,9]]},"DOI":"10.1007\/s10915-017-0387-x","type":"journal-article","created":{"date-parts":[[2017,2,16]],"date-time":"2017-02-16T14:51:38Z","timestamp":1487256698000},"page":"1021-1048","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Numerical Strategy for Freestream Preservation of the High Order Weighted Essentially Non-oscillatory Schemes on Stationary Curvilinear Grids"],"prefix":"10.1007","volume":"72","author":[{"given":"Yujie","family":"Zhu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6314-1423","authenticated-orcid":false,"given":"Zhensheng","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuxin","family":"Ren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,2,16]]},"reference":[{"issue":"2","key":"387_CR1","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/1061856031000104851","volume":"17","author":"CW Shu","year":"2003","unstructured":"Shu, C.W.: High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Int. J. Comput. Fluid Dyn. 17(2), 107\u2013118 (2003)","journal-title":"Int. J. Comput. Fluid Dyn."},{"issue":"1","key":"387_CR2","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0021-9991(92)90324-R","volume":"103","author":"SK Lele","year":"1992","unstructured":"Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103(1), 16\u201342 (1992)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"387_CR3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1006\/jcph.2000.6594","volume":"165","author":"XG Deng","year":"2000","unstructured":"Deng, X.G., Zhang, H.X.: Developing high-order weighted compact nonlinear schemes. J. Comput. Phys. 165(1), 22\u201344 (2000)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"387_CR4","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"GS Jiang","year":"1996","unstructured":"Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126(1), 202\u2013228 (1996)","journal-title":"J. Comput. Phys."},{"issue":"10","key":"387_CR5","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.2514\/3.61273","volume":"17","author":"PD Thomas","year":"1979","unstructured":"Thomas, P.D., Lombard, C.K.: Geometric conservation law and its application to flow computations on moving grids. AIAA J. 17(10), 1030\u20131037 (1979)","journal-title":"AIAA J."},{"key":"387_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(89)90063-6","volume":"81","author":"M Vinokur","year":"1989","unstructured":"Vinokur, M.: An analysis of finite-difference and finite-volume formulations of conservation laws. J. Comput. Phys. 81, 1\u201352 (1989)","journal-title":"J. Comput. Phys."},{"key":"387_CR7","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1006\/jcph.2002.7117","volume":"181","author":"RM Visbal","year":"2002","unstructured":"Visbal, R.M., Gaitonde, D.V.: On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155\u2013185 (2002)","journal-title":"J. Comput. Phys."},{"key":"387_CR8","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.compfluid.2009.08.005","volume":"39","author":"T Nonomura","year":"2010","unstructured":"Nonomura, T., Iizuka, N., Fujii, K.: Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids. Comput. Fluids 39, 197\u2013214 (2010)","journal-title":"Comput. Fluids"},{"key":"387_CR9","doi-asserted-by":"crossref","first-page":"2313","DOI":"10.1016\/j.jcp.2008.11.032","volume":"228","author":"S \u00c9tienne","year":"2009","unstructured":"\u00c9tienne, S., Garon, A., Pelletier, D.: Perspective on the geometric conservation law and finite element methods for ALE simulations of incompressible flow. J. Comput. Phys. 228, 2313\u20132333 (2009)","journal-title":"J. Comput. Phys."},{"key":"387_CR10","doi-asserted-by":"crossref","unstructured":"Trulio, J.G., Trigger, K.R.: Numerical solution of the one-dimensional hydrodynamic equations in an arbitrary time-dependent coordinate system. Technical Report UCLR-6522, University of California Lawrence Radiation laboratory (1961)","DOI":"10.2172\/4782302"},{"key":"387_CR11","doi-asserted-by":"crossref","unstructured":"Pulliam, T.H., Steger, J.L.: On implicit finite-difference simulations of three-dimensional flow. AIAA Paper 78\u201310 (1978)","DOI":"10.2514\/6.1978-10"},{"issue":"1","key":"387_CR12","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0045-7930(93)90003-R","volume":"22","author":"H Zhang","year":"1993","unstructured":"Zhang, H., Reggio, M., Tr\u00e9panier, J.Y., et al.: Discrete form of the GCL for moving meshes and its implementation in CFD schemes. Comput. Fluids 22(1), 9\u201323 (1993)","journal-title":"Comput. Fluids"},{"key":"387_CR13","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1006\/jcph.2001.6932","volume":"174","author":"C Farhat","year":"2001","unstructured":"Farhat, C., Geuzaine, P., Grandmont, C.: The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. J. Comput. Phys. 174, 669\u2013694 (2001)","journal-title":"J. Comput. Phys."},{"key":"387_CR14","doi-asserted-by":"crossref","unstructured":"Mavriplis, D.J., Yang, Z.: Achieving higher-order time accuracy for dynamic unstructured mesh fluid flow simulations: role of the GCL. AIAA Paper 2005\u20135114 (2005)","DOI":"10.2514\/6.2005-5114"},{"key":"387_CR15","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jcp.2014.01.045","volume":"265","author":"B Sj\u00f6green","year":"2014","unstructured":"Sj\u00f6green, B., Yee, H.C., Vinokur, M.: On high order finite-difference metric discretizations satisfying GCL on moving and deforming grids. J. Comput. Phys. 265, 211\u2013220 (2014)","journal-title":"J. Comput. Phys."},{"key":"387_CR16","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1016\/j.jcp.2010.10.028","volume":"230","author":"XG Deng","year":"2011","unstructured":"Deng, X.G., Mao, M.L., Tu, G.H., et al.: Geometric conservation law and applications to high-order finite difference schemes with stationary grids. J. Comput. Phys. 230, 1100\u20131115 (2011)","journal-title":"J. Comput. Phys."},{"key":"387_CR17","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.jcp.2012.12.002","volume":"239","author":"XG Deng","year":"2013","unstructured":"Deng, X.G., Min, Y.B., Mao, M.L., et al.: Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids. J. Comput. Phys. 239, 90\u2013111 (2013)","journal-title":"J. Comput. Phys."},{"key":"387_CR18","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.jcp.2012.08.031","volume":"232","author":"Y Abe","year":"2013","unstructured":"Abe, Y., Iizuka, N., Nonomura, T., et al.: Conservative metric evaluation for high-order finite difference schemes with the GCL identities on moving and deforming grids. J. Comput. Phys. 232, 14\u201321 (2013)","journal-title":"J. Comput. Phys."},{"key":"387_CR19","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.jcp.2013.12.019","volume":"260","author":"Y Abe","year":"2014","unstructured":"Abe, Y., Nonomura, T., Iizuka, N., et al.: Geometric interpretations and spatial symmetry property of metrics in the conservative form for high-order finite difference schemes on moving and deforming grids. J. Comput. Phys. 260, 163\u2013203 (2014)","journal-title":"J. Comput. Phys."},{"key":"387_CR20","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jcp.2014.12.040","volume":"284","author":"F Liao","year":"2014","unstructured":"Liao, F., Zhang, Z.Y., Zhang, L.X.: Extending geometric conservation law to cell-centered finite difference methods on stationary grids. J. Comput. Phys. 284, 419\u2013433 (2014)","journal-title":"J. Comput. Phys."},{"key":"387_CR21","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.compfluid.2015.04.015","volume":"116","author":"XD Deng","year":"2015","unstructured":"Deng, X.D., Jiang, Y., Mao, M.L., et al.: A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law. Comput. Fluids 116, 29\u201345 (2015)","journal-title":"Comput. Fluids"},{"key":"387_CR22","doi-asserted-by":"crossref","unstructured":"Cai, X., Ladeinde, F.: Performance of WENO scheme in generalized curvilinear coordinate systems. AIAA Paper 2008\u201336 (2008)","DOI":"10.2514\/6.2008-36"},{"issue":"2","key":"387_CR23","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1137\/120889885","volume":"35","author":"Y Jiang","year":"2013","unstructured":"Jiang, Y., Shu, C.W., Zhang, M.: An alternative formulation of finite difference weighted ENO schemes with Lax\u2013Wendroff time discretization for conservation laws. SIAM J. Sci. Comput. 35(2), 1137\u20131160 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"387_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4310\/MAA.2014.v21.n1.a1","volume":"v21","author":"Y Jiang","year":"2014","unstructured":"Jiang, Y., Shu, C.W., Zhang, M.: Free-stream preserving finite difference schemes on curvilinear meshes. Methods Appl. Anal. v21, 1\u201330 (2014)","journal-title":"Methods Appl. Anal."},{"key":"387_CR25","unstructured":"Asahara, M., Nonomura, T., Fujii, K. et al.: Comparison of resolution and robustness with TSFDWENO schemes. In: Proceedings of 27th Computational Fluid Dynamics Symposium, C03-4, (2013) (in Japanese)"},{"key":"387_CR26","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.compfluid.2014.09.025","volume":"107","author":"T Nonomura","year":"2015","unstructured":"Nonomura, T., Terakado, D., Abe, Y., et al.: A new technique for freestream preservation of finite-difference WENO on curvilinear grid. Comput. Fluids 107, 242\u2013255 (2015)","journal-title":"Comput. Fluids"},{"key":"387_CR27","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0021-9991(84)90142-6","volume":"54","author":"P Woodward","year":"1984","unstructured":"Woodward, P., Colella, P.: The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54, 115\u2013173 (1984)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0387-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0387-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0387-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,24]],"date-time":"2022-07-24T08:24:08Z","timestamp":1658651048000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0387-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,16]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["387"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0387-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,16]]}}}