A numerical solution of the Navier-Stokes equations using the finite element technique. (English) Zbl 0328.76020


76D05 Navier-Stokes equations for incompressible viscous fluids
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
Full Text: DOI


[1] Oden, J.T., The finite element method in fluid mechanics, Lecture for NATO advanced study institute on finite element methods in continuum mechanics, (1971), Lisbon · Zbl 0226.65051
[2] Hood, P., A finite element solution of the Navier-Stokes equations for incompressible contained flow, () · Zbl 0328.76020
[3] Cheng, S.I., Numerical integration of Navier-Stokes equations, Aiaa jl, 8, 2115-2122, (1970)
[4] Zienkiewics, O.C.; Cheung, Y.K., Finite elements in the solution of field problems, The engineer, 220, 507-510, (1965)
[5] de Vries, G.; Norrie, D.H., The application of the finite element technique to potential flow problems, Trans. ASME appl. mech. div., paper no. 71-APM-22, 798-802, (1971) · Zbl 0228.76038
[6] Ergatoudis, J.; Irons, B.M.; Zienkiewicz, O.C., Curved isoparametric, quadrilateral elements for finite element analysis, Int. J. solids struct., 4, 31-42, (1968) · Zbl 0152.42802
[7] Irons, B.M., A conforming quartic triangular element for plate bending, Int. J. num. meth. engng, 1, 29-45, (1969) · Zbl 0247.73071
[8] Zenisek, A., Interpolation polynomials on the triangle, Numer. math., 15, 283-296, (1970) · Zbl 0216.38901
[9] Hussey, M.J.L.; Thatcher, R.W.; Bernal, M.J.M., On the construction and use of finite elements, J. inst. maths. applics., 6, 263-282, (1970) · Zbl 0211.47502
[10] Zienkiewicz, O.C., ()
[11] Oden, J.T., A general theory of finite elements II applications, Int. J. num. meth. engng, 1, 247-259, (1969) · Zbl 0263.73048
[12] Tong, P., The finite element method for fluid flow, paper US5-4, ()
[13] Finlayson, B.A.; Scriven, L.E., The method of weighted residuals and its relation to certain variational principles for the analysis of transport processess, Chem. engng sci., 20, 395-404, (1965)
[14] Finlayson, B.A.; Scriven, L.E., The method of weighted residuals—a review, Appl. mech. rev., 19, 735-748, (1966)
[15] Finlayson, B.A.; Scriven, L.E., On the search for variational principles, Int. J. heat mass transfer, 10, 799-821, (1961) · Zbl 0148.44102
[16] J. Davis, and P. Hood, Finite element formulation with reference to fluid dynamics, To be published. · Zbl 0309.76023
[17] Baker, A.J., Finite element theory for viscous fluid dynamics, () · Zbl 0255.76042
[18] Baker, A.J., Finite element computational theory for three dimensional boundary layer flow, (), San Diego, California · Zbl 0291.76016
[19] J. Davis; C. Taylor, Finite element solution of the tidal hydraulic equations, To be published.
[20] Schlichting, H., Boundary layer theory, (1960), McGraw-Hill New York · Zbl 0096.20105
[21] Taylor, R.L., On completeness of shape functions for finite element analysis, Int. J. num. meth. engng, 4, 17-22, (1972) · Zbl 0255.73095
[22] Spreeuw, E., Fiesta: finite elements stress and temperature anlysis, Reactor centrum nederland rep. RCN-149, (1971)
[23] Card, C.C.H., ()
[24] Atkinson, B.; Card, C.C.H.; Irons, B.M., Application of the finite element method to creeping flow problems, Trans. instn chem. engrs, 48, T276-T284, (1970)
[25] Atkinson, B.; Brocklebank, M.P.; Card, C.C.H.; Smith, J.M., Low Reynolds number developing flows, A.I.ch.E. jl, 15, 548-553, (1969)
[26] Zienkiewicz, O.C.; Taylor, C., Weighted residual processes in F.E.M. with particular reference to some coupled and transient problems, Lecture for NATO advanced study institute on finite element methods in continuum mechanics, (1971), Lisbon
[27] Bird, R.B., New variational principle for incompressible non-Newtonian flow, Phys. fluids, 3, 539-541, (1960) · Zbl 0094.38802
[28] B. Atkinson, Private Communication, University of Wales, Swansea (1972).
[29] Kikuchi, F.; Ando, Y., A finite element method for initial value problems, ()
[30] Zienkiewicz, O.C.; Parekh, C.J., Transient field problems: two dimensional and three dimensionial analysis by isoparametric finite elements, Int. J. num. meth. engng, 2, 61-71, (1970) · Zbl 0262.73072
[31] Tong, P.; Fung, Y.C., Slow particulate viscous flow in channels and tubes-application to biomechanics, Trans. ASME appl. mech. div., paper no. 71-APM-R, 721-728, (1971) · Zbl 0224.76108
[32] Stark, K.P., A numerical study of the non-linear laminar regime of flow in an idealised porous medium, ()
[33] Mills, R.D., Numerical solution of the viscous flow equations for a class of closed flows, Jl. R.aeronaut. soc., 69, 714-718, (1965)
[34] Burggraf, O.R., Analytic and numerical studies of the structure of steady separated flows, J. fluid mech., 24, 113-151, (1966)
[35] P. Hood, Ph. D. Thesis, University of Wales, Swansea. To be submitted.
[36] Bogner, F.K.; Fox, R.L.; Schmit, L.A., The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas, () · Zbl 0159.55806
[37] Taneda, S., Experimental investigation of the akes behind cylinders and plates at low Reynolds numbers, J. phys. soc. Japan, 11, 302-307, (1956)
[38] Kawaguti, M.; Jain, P., Numerical study of a viscous fluid flow past a circular cylinder, J. phys. soc. Japan, 21, 2055-2062, (1966)
[39] Dennis, S.C.R.; Chang, G.Z., Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J. fluid mech., 42, 471-489, (1970) · Zbl 0193.26202
[40] Takami, H.; Keller, H.B., Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder, Phys. fluids, Suppl. II, II-51-II-56, (1969) · Zbl 0206.55004
[41] Jain, P.C.; Rao, K.S., Numerical solution of unsteady viscous incompressible flow past a circular cylinder, Phys. fluids, Suppl. II, II-57-II-64, (1969) · Zbl 0206.55005
[42] Thoman, D.C.; Szewczyk, A.A., Time dependent viscous flow over a circular cylinder, Phys. fluids, Suppl. II, II-76-II-86, (1969) · Zbl 0208.55302
[43] Olson, M.D., A variational finite element method for two-dimensional steady viscous flows, mcgill university engineering institute of Canada, ()
[44] Kan, D., Mesh and contour plot for triangle and isoparametric elements, (), Dept. Civil Engineering
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