{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T10:11:22Z","timestamp":1694599882384},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,12,4]],"date-time":"2006-12-04T00:00:00Z","timestamp":1165190400000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc Appl Math and Mech"],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Three\u2010dimensional (3D) simulations of blood flow in medium to large vessels are now a common practice. These models consist of the 3D Navier\u2010Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall structure. However, it is still computationally unaffordable to simulate very large sections, let alone the whole, of the human circulatory system with fully 3D fluid\u2010structure interaction models. Thus truncated 3D regions have to be considered.<\/jats:p><jats:p>Reduced models, one\u2010dimensional (1D) or zero\u2010dimensional (0D), can be used to approximate the remaining parts of the cardiovascular system at a low computational cost. These models have a lower level of accuracy, since they describe the evolution of averaged quantities, nevertheless they provide useful information which can be fed to the more complex model. More precisely, the 1D models describe the wave propagation nature of blood flow and coupled with the 3D models can act also as absorbing boundary conditions.<\/jats:p><jats:p>We consider in this work the coupling of a 3D fluid\u2010structure interaction model with a 1D hyperbolic model. We study the stability of the coupling and present some numerical results. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/pamm.200610008","type":"journal-article","created":{"date-parts":[[2006,12,4]],"date-time":"2006-12-04T11:38:31Z","timestamp":1165232311000},"page":"27-30","source":"Crossref","is-referenced-by-count":5,"title":["Coupling 3D and 1D fluid\u2010structure interaction models for blood flow simulations"],"prefix":"10.1002","volume":"6","author":[{"given":"L.","family":"Formaggia","sequence":"first","affiliation":[]},{"given":"A.","family":"Moura","sequence":"additional","affiliation":[]},{"given":"F.","family":"Nobile","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,4]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"R.Temam Navier\u2010Stokes equations and nonnlinear functional analysis Regional Conferences Series in Applied Mathematics (Society for Industrial and Applied Mathematics 1995).","DOI":"10.1137\/1.9781611970050"},{"issue":"181","key":"e_1_2_1_3_2","first-page":"179","article-title":"Nonlinear partial differential equations and their applications","author":"Begue C.","year":"1986","journal-title":"Collge de France Seminar"},{"issue":"2","key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"279","DOI":"10.4099\/math1924.20.279","volume":"20","author":"Conca C.","year":"1994","journal-title":"Japan J. Math."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00302-4"},{"key":"e_1_2_1_6_2","unstructured":"L.FormaggiaandA.Veneziani Reduced and multiscale models for the human cardiovascular system Lecture notes VKI Lecture Series 2003\u201007 Brussels (2003)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050030"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2004.04.021"},{"key":"e_1_2_1_9_2","unstructured":"L.FormaggiaandF.Nobile East\u2010West Journal of Numerical Mathematics 7 105\u2013132(1999)."},{"key":"e_1_2_1_10_2","unstructured":"L.Formaggia A.Moura F.Nobile in preparation."},{"key":"e_1_2_1_11_2","unstructured":"http:\/\/www.lifev.org\/."}],"container-title":["PAMM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fpamm.200610008","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pamm.200610008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T13:08:26Z","timestamp":1694524106000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pamm.200610008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["10.1002\/pamm.200610008"],"URL":"https:\/\/doi.org\/10.1002\/pamm.200610008","archive":["Portico"],"relation":{},"ISSN":["1617-7061","1617-7061"],"issn-type":[{"value":"1617-7061","type":"print"},{"value":"1617-7061","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}