Finite element solution of the unsteady Navier-Stokes equations by a fractional step method. (English) Zbl 0481.76037

Donea, J.; Giuliani, S.; Laval, H.; Quartapelle, L.

Comput. Methods Appl. Mech. Eng. 30, 53-73 (1982).

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
76M99	Basic methods in fluid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

unsteady; fractional step method; time-dependent

References:

[1]	Heinrich, J. C.; Marshall, R. S.; Zienkiewicz, O. C., Penalty function solution of coupled convective and conductive heat transfer, (Proc. 1st Internat. Conf. Numer. Meths. in Laminar and Turbulent (1978), Flow, Swansea: Flow, Swansea U.K)
[2]	Malkus, D. S.; Hughes, T. J.R., Mixed finite element methods—reduced and selective integration techniques: A unification of concepts, Comput. Meths. Appl. Mech. Engrg., 15, 63-81 (1978) · Zbl 0381.73075
[3]	Hughes, T. J.R.; Liu, W. K.; Brooks, A., Finite element analysis of incompressible viscous flows by the penalty function formulation, J. Comput. Phys., 30, 1-60 (1979) · Zbl 0412.76023
[4]	Bercovier, M.; Engelman, M., A finite element for the numerical solution of viscous incompressible flows, J. Comput. Phys., 30, 181-201 (1979) · Zbl 0395.76040
[5]	Fortin, M.; Thomasset, F., Mixed finite-element methods for incompressible flow problems, J. Comput. Phys., 31, 113-145 (1979) · Zbl 0395.76023
[6]	Christie, I.; Griffiths, D. F.; Mitchell, A. R.; Zienkiewicz, O. C., Finite element methods for second order differential equations with significant first derivatives Internat, J. Numer. Meths. Engrg, 10, 1389-1396 (1976) · Zbl 0342.65065
[7]	Heinrich, J. C.; Huyakorn, P. S.; Zienkiewicz, O. C.; Mitchell, A. R., An upwind finite element scheme for two-dimensional convective-transport equation Internat, J. Numer. Meths. Engrg., 11, 113-143 (1977) · Zbl 0353.65065
[8]	(Hughes, T. J.R., Finite Element Methods for Convection Dominated Flows. Finite Element Methods for Convection Dominated Flows, ADM, Vol. 34 (1979), ASME: ASME New York)
[9]	Baker, A. J., A highly stable explicit integration technique for computational continuum mechanics, (Connors, J. J.; Brebbia, C. A., Numerical Methods in Fluid Dynamics (1974), Pentech: Pentech London)
[10]	Gresho, P. M.; Lee, R. L.; Stullich, T. W.; Sani, R. L., Solution of the time-dependent Navier-Stokes equations via FEM, (Second Internat. Conf. on Finite Elements in Water Resources. Second Internat. Conf. on Finite Elements in Water Resources, London (1978)) · Zbl 0446.76034
[11]	Smith, S. L.; Brebbia, C. A., Improved stability techniques for the solution of Navier-Stokes equations, Appl. Math. Modeling, 1, 226-234 (1977) · Zbl 0362.76002
[12]	Temam, R., On the Theory and Numerical Analysis of the Navier-Stokes Equations (1977), North-Holland: North-Holland Amsterdam · Zbl 0383.35057
[13]	Tuann, S. Y.; Olson, M. D., Review of computing methods for recirculating flows, J. Comput. Phys., 29, 1-19 (1978) · Zbl 0427.76028
[14]	Chorin, A. J., Numerical solution of the Navier-Stokes equations, Math. Comput., 22, 745-762 (1968) · Zbl 0198.50103
[15]	Batchelor, G. K., An Introduction to Fluid Dynamics (1967), Cambridge University Press: Cambridge University Press London · Zbl 0152.44402
[16]	Raviart, P. A., Méthodes d’éléments finis en mécanique des fluides, Cours de l’Ecole d’Eté d’Analyse Numérique (1979)
[17]	Chorin, A. J., On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comput., 23, 341-353 (1969) · Zbl 0184.20103
[18]	Donea, J.; Giuliani, S.; Morgan, K.; Quartapelle, L., The significance of the chequerboarding in Galerkin finite element solutions of the Navier-Stokes equations Internat, J. Numer. Meths. Engrg., 17, 790-795 (1981) · Zbl 0461.76018
[19]	Zienkiewicz, O. C., The Finite Element Method (1977), McGraw-Hill: McGraw-Hill London · Zbl 0435.73072
[20]	Gresho, P. M.; Lee, R. L.; Sani, R., Advection-dominated flows with emphasis on the consequences of mass lumping, (Finite Elements in Fluids, Vol. 3 (1978), Wiley: Wiley New York) · Zbl 0442.76067
[21]	Donea, J.; Giuliani, S., A simple method to generate high-order accurate convection operators for explicit schemes based on linear finite elements Internat, J. Numer. Meths. Fluids, 1, 63-79 (1981) · Zbl 0461.76068
[22]	Donea, J.; Giuliani, S.; Laval, H.; Quartapelle, L., Solution of the unsteady Navier-Stokes equations by a finite-element projection method, (Taylor, C.; Morgan, K., Recent Advances in Numerical Methods in Fluids, Vol. 2 (1981), Pineridge: Pineridge Swansea) · Zbl 0481.76037
[23]	Krieg, R. D.; Key, S. W., Transient shell response by numerical time integration Internat, J. Numer. Meths. Engrg., 7, 273-286 (1973)
[24]	Donea, J.; Guiliani, S., The computer code CONDIF for transient convective-conductive heat transfer, EUR 6822/I and II EN (1980)
[25]	Laval, H., CONVEC, A computer program for transient incompressible fluid flow based on quadratic finite elements, EUR 7427/I and II EN (1981)
[26]	Burggraf, O., Analytical and numerical studies of the structure of steady separated flows, J. Fluid Mech., 24, 113-151 (1966)
[27]	Quartapelle, L., Vorticity conditioning in the computation of two-dimensional viscous flows, J. Comput. Phys., 40, 453-477 (1981) · Zbl 0472.76062
[28]	Macagno, E.; Hung, T. K., Computational and experimental study of a captive annular eddy, J. Fluid Mech., 28, 43-64 (1967)
[29]	Dennis, S. C.R.; Walker, J. D.A., Calculation of the steady flow past a sphere at low and moderate Reynolds numbers, J. Fluid Mech., 48, 771-789 (1971) · Zbl 0266.76023
[30]	Kee, R. J.; Landram, S. C.; Miles, J. C., Natural convection of a heat-generating fluid within closed vertical cylinders and spheres, Trans. ASME Ser. C, 55-61 (1976)