zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. (English) Zbl 1007.74035
Summary: For the analysis of flows in compliant vessels, we propose an approach to couple the original three-dimensional equations with a convenient one-dimensional model. This multi-scale strategy allows for a dramatic reduction of computational complexity, and is suitable for “absorbing” outgoing pressure waves. In particular, it is of interest for the description of blood motion in the arterial system.

74F10Fluid-solid interactions
76D05Navier-Stokes equations (fluid dynamics)
76Z05Physiological flows
74S05Finite element methods in solid mechanics
Full Text: DOI
[1] Ciarlet, P. G.: Introduction to linear shell theory. (1998) · Zbl 0912.73001
[2] G.R. Cokelet, The rheology and tube flow of blood, in: R. Skalak, S. Chen (Eds.), Handbook of Bioengineering, McGraw-Hill, New York, 1987
[3] Engquist, B.; Majda, A.: Numerical radiation boundary conditions for unsteady transonic flow. J. comput. Phys. 40, No. 1, 91-103 (1981) · Zbl 0467.76056
[4] L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni, Numerical treatment of defective boundary conditions for the Navier--Stokes equation, INRIA Research Report No. 4093, January 2001 · Zbl 1020.35070
[5] Formaggia, L.; Nobile, F.; Quarteroni, A.; Veneziani, A.: Multiscale modelling of the circolatory system: a preliminary analysis. Comp. vis. Science 2, 75-83 (1999) · Zbl 1067.76624
[6] Giles, M. B.: Non-reflecting boundary conditions for Euler equation calculations. Aiaa j. 28, No. 12, 2050-2058 (1990)
[7] Givoli, D.: Non-reflecting boundary conditions. J. comput. Phys. 94, 1-29 (1991) · Zbl 0731.65109
[8] E. Godlewski, P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Applied Mathematical Sciences, vol. 118, Springer, New York, 1996 · Zbl 0860.65075
[9] Hayashi, K.; Handa, K.; Nagasawa, S.; Okumura, A.: Stiffness and elastic behaviour of human intracranial and extracranial arteries. J. biomech. 13, 175-184 (1980)
[10] Heywood, J. G.; Rannacher, R.; Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier--Stokes equations. Int. J. Numer. methods fluids 22, 325-352 (1996) · Zbl 0863.76016
[11] Hughes, T. J.: The finite element method, linear static and dynamic finite element analysis. (1987) · Zbl 0634.73056
[12] Langewouters, G. L.; Wesseling, K. H.; Goedhard, W. J. A.: The elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J. biomech. 17, 425-435 (1984)
[13] D.A. McDonald, Blood Flow in Arteries, third ed. edited by W.W. Nichols, M.F. O’Rourke, Edward Arnold, London, 1990
[14] Mittal, S.; Tezduyar, T. E.: Parallel finite element simulation of 3D incompressible flows: fluid--structure interactions. Int. J. Numer. methods fluids 21, 933-953 (1995) · Zbl 0873.76047
[15] F. Nobile, Fluid--structure interaction problems in hemodynamics, Master’s Thesis, Technical University of Milan, 1998 (in Italian)
[16] Perktold, K.; Resch, M.; Florian, H.: Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model. ASME J. Biomech. engrg. 113, 463-475 (1991)
[17] Quarteroni, A.; Tuveri, M.; Veneziani, A.: Computational vascular fluid dynamics: problems, models and methods. Comp. vis. Science 2, 163-197 (2000) · Zbl 1096.76042
[18] A. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Springer Series in Computational Mathematics, vol. 23, Springer, Berlin, 1994 · Zbl 0803.65088
[19] Reismann, H.: Elastic plates: theory and application. (1988) · Zbl 0761.73002
[20] Simo, J. C.; Fox, D. D.: On a stress resultant geometrically exact shell model, part I: Formulation and optimal parametrization. Comput. methods appl. Mech. engrg. 72, 267-304 (1989) · Zbl 0692.73062
[21] Simo, J. C.; Fox, D. D.; Rifai, M. S.: On a stress resultant geometrically exact shell model, part II: The linear theory; computational aspects. Comput. methods appl. Mech. engrg. 73, 53-92 (1989) · Zbl 0724.73138
[22] Simo, J. C.; Fox, D. D.; Rifai, M. S.: On a stress resultant geometrically exact shell model, part III: Computational aspects of the nonlinear theory. Comput. methods appl. Mech. engrg. 79, 21-70 (1989) · Zbl 0746.73015
[23] Tijsseling, A. S.: Fluid--structure interaction in liquid filled pipe systems: a review. J. fluids struct. 10, 109-146 (1996)
[24] Tozeren, A.: Elastic properties of arteries and their influence on the cardiovascular system. ASME J. Biomech. engrg. 106, 182-185 (1984)
[25] A. Veneziani, Mathematical and numerical modelling of blood flow problems, Ph.D. Thesis, University of Milan, 1998 · Zbl 1075.76699
[26] Xu, X. Y.; Collins, M. W.; Jones, C. J. H.: Flow studies in canine aortas. ASME J. Biomech. engrg. 114, No. 11, 504-511 (1992)