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


MSC:

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
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[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, (M. Sc. Thesis (1970), University of Wales: University of Wales Swansea) · 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., (The Finite Element Method in Engineering Science (1971), McGraw-Hill: McGraw-Hill New York) · Zbl 0237.73071
[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, (Gallagher, R. H., Japan-U.S. Seminar on Matrix Methods in Structural Analysis and Design (1970), University of Alabama Press)
[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.; 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, (Rep. No. 9500-920189 (1970), Bell Aerospace Company) · Zbl 0255.76042
[18] Baker, A. J., Finite element computational theory for three dimensional boundary layer flow, (Presented at the AIAA 10th Aerospace Sci. Mtg. Presented at the AIAA 10th Aerospace Sci. Mtg, AIAA Reprint No. 72-108 (1972)), San Diego, California · Zbl 0291.76016
[19] J. Davis; C. Taylor, Finite element solution of the tidal hydraulic equations, To be published.; J. Davis; C. Taylor, Finite element solution of the tidal hydraulic equations, To be published.
[20] Schlichting, H., Boundary Layer Theory (1960), McGraw-Hill: 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., (Ph. D. Thesis (1968), University of Wales: University of Wales Swansea)
[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).; B. Atkinson, Private Communication, University of Wales, Swansea (1972).
[29] Kikuchi, F.; Ando, Y., A finite element method for initial value problems, (Proc. 3rd Conf. on Matrix Methods in Structural Mechanics (1971), Wright Patterson Air Force Base: Wright Patterson Air Force Base Ohio)
[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, (International Association for Hydraulic Research Symposium on the Fundamentals of Transport Phenomena (1969), Porous Media: Porous Media Hafia, Israel)
[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.; 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, (The Conference of Matrix Methods in Structural Mechanics (1965), Wright Patterson Air Force Base: Wright Patterson Air Force Base Ohio) · 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, (Conf. on Finite Element Methods in Civil Engineering (1972), McGill University: McGill University Montreal, Quebec)
[44] Kan, D., Mesh and Contour plot for triangle and isoparametric elements, (Computer Rep. No. CNME/CR/39 (1970), University of Wales: University of Wales Swansea), Dept. Civil Engineering
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