{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:30Z","timestamp":1740123570249,"version":"3.37.3"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,3,11]],"date-time":"2019-03-11T00:00:00Z","timestamp":1552262400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100012555","name":"Russian Foundation for Fundamental Investigations","doi-asserted-by":"publisher","award":["96-01-01577"],"award-info":[{"award-number":["96-01-01577"]}],"id":[{"id":"10.13039\/100012555","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":[[2019,12]]},"DOI":"10.1007\/s10915-019-00926-1","type":"journal-article","created":{"date-parts":[[2019,3,11]],"date-time":"2019-03-11T14:21:30Z","timestamp":1552314090000},"page":"1136-1149","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Iteration-Free Approach to Solving the Navier\u2013Stokes Equations by Implicit Finite Difference Schemes in the Vorticity-Stream Function Formulation"],"prefix":"10.1007","volume":"81","author":[{"given":"V. S.","family":"Ryaben\u2019kii","sequence":"first","affiliation":[]},{"given":"V. A.","family":"Torgashov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,3,11]]},"reference":[{"key":"926_CR1","volume-title":"Computational Fluid Mechanics and Heat Transfer. Series in Computational Methods in Mechanics and Thermal Sciences","author":"DA Anderson","year":"1984","unstructured":"Anderson, D.A., Tannehill, J.C., Pletcher, R.H.: Computational Fluid Mechanics and Heat Transfer. Series in Computational Methods in Mechanics and Thermal Sciences. Hemisphere Publishing Corp., Washington, DC (1984)"},{"key":"926_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58239-4","volume-title":"Computational Techniques for Fluid Dynamics. Specific Techniques for Different Flow Categories. Springer Series in Computational Physics","author":"CAJ Fletcher","year":"1991","unstructured":"Fletcher, C.A.J.: Computational Techniques for Fluid Dynamics. Specific Techniques for Different Flow Categories. Springer Series in Computational Physics, 2nd edn. Springer, Berlin (1991). \nhttps:\/\/doi.org\/10.1007\/978-3-642-58239-4","edition":"2"},{"issue":"3","key":"926_CR3","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/0021-9991(82)90058-4","volume":"48","author":"U Ghia","year":"1982","unstructured":"Ghia, U., Ghia, K.N., Shin, C.T.: High-Re solutions for incompressible flow using the Navier\u2013Stokes equations and a multigrid method. J. Comput. Phys. 48(3), 387\u2013411 (1982). \nhttps:\/\/doi.org\/10.1016\/0021-9991(82)90058-4\n\n. \nhttp:\/\/www.sciencedirect.com\/science\/article\/pii\/0021999182900584","journal-title":"Journal of Computational Physics"},{"issue":"5","key":"926_CR4","first-page":"1180","volume":"21","author":"BD Moiseenko","year":"1981","unstructured":"Moiseenko, B.D., Fryazinov, I.V.: Conservative difference schemes for equations of an incompressible viscous fluid in Euler variables. Zhurnal Vychisl. Mat. i Mat. Fiz. 21(5), 1180\u20131191 (1981)","journal-title":"Zhurnal Vychisl. Mat. i Mat. Fiz."},{"key":"926_CR5","volume-title":"Computational Fluid Mechanics and Heat Transfer, Series in Computational and Physical Processes in Mechanics and Thermal Sciences","author":"RH Pletcher","year":"2013","unstructured":"Pletcher, R.H., Tannehill, J.C., Anderson, D.A.: Computational Fluid Mechanics and Heat Transfer, Series in Computational and Physical Processes in Mechanics and Thermal Sciences, 3rd edn. CRC Press, Boca Raton (2013)","edition":"3"},{"key":"#cr-split#-926_CR6.1","unstructured":"Roache, P.J.: Computational Fluid Dynamics. Hermosa Publishers, Albuquerque, NM (1976). With an appendix (\"On artificial viscosity\") reprinted from J. Comput. Phys. 10"},{"key":"#cr-split#-926_CR6.2","unstructured":"(2) 169-184 (1972), Revised printing"},{"key":"926_CR7","volume-title":"Fundamentals of Computational Fluid Dynamics","author":"PJ Roache","year":"1998","unstructured":"Roache, P.J.: Fundamentals of Computational Fluid Dynamics. Hermosa Publishers, Albuquerque (1998)"},{"key":"926_CR8","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1070\/RM1971v026n03ABEH003836","volume":"26","author":"VS Ryaben\u2019kii","year":"1971","unstructured":"Ryaben\u2019kii, V.S.: The method of internal boundary conditions in the theory of boundary value difference problems. Russ. Math. Surv. 26, 117\u2013176 (1971)","journal-title":"Russ. Math. Surv."},{"key":"926_CR9","volume-title":"Difference Potentials Method for Some Problems of Continuous Media Mechanics","author":"VS Ryaben\u2019kii","year":"1987","unstructured":"Ryaben\u2019kii, V.S.: Difference Potentials Method for Some Problems of Continuous Media Mechanics. Nauka, Moscow (1987). (In Russian)"},{"key":"926_CR10","volume-title":"Introduction to Computational Mathematics [Vvedenie v vychislitel\u2019nuyu matematiku]","author":"VS Ryaben\u2019kii","year":"1994","unstructured":"Ryaben\u2019kii, V.S.: Introduction to Computational Mathematics [Vvedenie v vychislitel\u2019nuyu matematiku]. Fizmatlit \u201cNauka\u201d, Moscow (1994). [Russian]"},{"key":"926_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56344-7","volume-title":"Method of Difference Potentials and Its Applications, Springer Series in Computational Mathematics","author":"VS Ryaben\u2019kii","year":"2002","unstructured":"Ryaben\u2019kii, V.S.: Method of Difference Potentials and Its Applications, Springer Series in Computational Mathematics, vol. 30. Springer, Berlin (2002)"},{"issue":"10","key":"926_CR12","first-page":"100","volume":"8","author":"VS Ryaben\u2019kii","year":"1996","unstructured":"Ryaben\u2019kii, V.S., Torgashov, V.A.: A noniterative method for solving an implicit difference scheme for Navier\u2013Stokes equations in vorticity-stream function variables. Mat. Model. 8(10), 100\u2013112 (1996). [in Russian]","journal-title":"Mat. Model."},{"key":"926_CR13","volume-title":"A Theoretical Introduction to Numerical Analysis","author":"VS Ryaben\u2019kii","year":"2007","unstructured":"Ryaben\u2019kii, V.S., Tsynkov, S.V.: A Theoretical Introduction to Numerical Analysis. Chapman & Hall\/CRC, Boca Raton (2007)"},{"key":"926_CR14","unstructured":"\u0420\u044f\u0431\u0435\u043d\u044c\u043a\u0438\u0439, \u0412.\u0421., \u0422\u043e\u0440\u0433\u0430\u0448\u043e\u0432, \u0412.\u0410.: \u0411\u0435\u0437\u044b\u0442\u0435\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0435\u044f\u0432\u043d\u043e\u0439 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u043d\u043e\u0439 \u0441\u0445\u0435\u043c\u044b \u0434\u043b\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u041d\u0430\u0432\u044c\u0435-\u0421\u0442\u043e\u043a\u0441\u0430 \u0432 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445: \u0437\u0430\u0432\u0438\u0445\u0440\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0442\u043e\u043a\u0430. \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u041c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 8(10), 100\u2013112 (1996)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00926-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-019-00926-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00926-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T00:06:10Z","timestamp":1583798770000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-019-00926-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,11]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["926"],"URL":"https:\/\/doi.org\/10.1007\/s10915-019-00926-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2019,3,11]]},"assertion":[{"value":"29 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 February 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}