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Liu, N. S.; Krause, E.

Calculation of incompressible viscous flows in vessels with moving boundaries. (English) Zbl 0423.76020

Acta Mech. 33, 21-32 (1979).
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scan of Zbl 0423.76020

Cited in 1 Review
Cited in 2 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65Z05 Applications to the sciences

Keywords:

incompressible viscous flows; vessels; moving boundaries; three- dimensional; unsteady; moderate Reynolds numbers; Navier Stokes equations; curvilinear coordinates; convergence and stability; matching technique; plane Poiseuille flow; curved pipe
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References:

[1] Peskin, C. S.: Mathematical aspects of heart physiology. (Lecture Notes.) Courant Institute of Mathematical Sciences, New York University, 1975. · Zbl 0301.92001
[2] Cheng, S. I.: A critical review of the numerical solution of Navier-Stokes equations. (Lecture Series 63.) von Karman Institute for Fluid Dynamics. 1974.
[3] Viecelli, J. A.: A computing method for incompressible flows bounded by moving walls. J. Comp. Phys.8, 119 (1971). · Zbl 0222.76033 · doi:10.1016/0021-9991(71)90039-8
[4] Hirt, C. W., Harlow, F. H.: A general corrective procedure for the numerical solution of initial-value problems. J. Comp. Phys.2, 114 (1967). · Zbl 0155.20503 · doi:10.1016/0021-9991(67)90029-0
[5] Dorodnicyn, A. A.: Review of methods for solving the Navier-Stokes equations. Proc. 3rd ICFD (Lecture Notes in Physics 18), p. 1. Berlin-Heidelberg-New York: Springer. 1972.
[6] Thoman, D. C., Szewczyk, A. A.: Time dependent viscous flow over a circular cylinder. The physics of Fluids, Suppl.II, 76 (1969). · Zbl 0208.55302
[7] Daly, B. J.: Pulsatile flow through a tube containing rigid and distensible sections. Proc. 5th ICFD (Lecture Notes in Physics, 59), p. 153. Berlin-Heidelberg-New York: Springer. 1976. · Zbl 0382.76098
[8] Liu, N. S.: Numerische Integration der Navier-Stokes Gleichungen für inkompressible, dreidimensionale Strömungen in Gefäßen mit dehnbaren Wänden. Diss., RWTH Aachen, 1977.
[9] Liu, N. S.: Finite-difference solution of the Navier-Stokes equations for incompressible three-dimensional flows. Proc. 5th ICFD (Lecture Notes in Physics, 59), p. 300. Berlin-Heidelberg-New York: Springer. 1976. · Zbl 0358.76024
[10] Liu, N. S.: Numerical integration of the Navier-Stokes equation for incompressible three-dimensional flows through vessels with flexible walls. Paper presented at the 2nd GAMM-Conference on numerical methods in Fluid Mech., October 11-13, 1977, Köln-Porz, Germany. (Published in Proc. 2nd GAMM-Conference on Numerical Method in Fluid Mechanics.)
[11] Liu, N. S.: Developing flow in a curved pipe. Paper presented at Euromech 92. Cardiovascular and pulmonary dynamics, September 5-8, 1977, Compiegne, France. (Published in INSERM Colloquium Proc. Series.)
[12] Sokolnikoff, I. S.: Tensor Analysis, 2nd edition, p. 133. New York: J. Wiley. 1964. · Zbl 0121.38204
[13] Patel, D. J., Greenfield, J. C., Fry, D. L.: In vivo pressure-length-radius relationship of certain blood vessels in man and dog. Pulsatile blood flow. New York: McGraw-Hill. 1964.
[14] Ling, S. C., Atabek, H. B.: A nonlinear analysis of pulsatile flow in arteries. J. Fluid Mech.55, 493 (1972). · Zbl 0246.76126 · doi:10.1017/S0022112072001971
[15] Williams, G. P.: Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow. J. Fluid Mech.37, 727 (1969). · Zbl 0183.55104 · doi:10.1017/S002211206900084X
[16] Chorin, A. J.: Numerical solution of the Navier-Stokes equations. Math. of Comp.22, 745 (1968). · Zbl 0198.50103 · doi:10.1090/S0025-5718-1968-0242392-2
[17] Isaacson, E., Keller, H. B.: Analyse numerischer Verfahren, 1st ed., p. 437, P. 90. Zürich-Frankfurt/M.: Verlag Harri Deutsch. 1973. · Zbl 0254.65001
[18] Hirt, C. W., Cook, J. L.: Calculating three-dimensional flows around structures and over rough terrain. J. Comp. Phys.10, 324 (1972). · Zbl 0251.76017 · doi:10.1016/0021-9991(72)90070-8
[19] Krause, E.: Numerische Lösung der Navier-Stokes-Gleichungen zur Berechnung inkompressibler Zentrifugenströmungen. Paper presented at the DFVLR-Colloquium ?Strömungsmechanische Vorgänge in Gaszentrifugen?, May 14, 1970, Porz-Wahn, Germany.
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