×

zbMATH — the first resource for mathematics

Numerical method for unsteady 3D Navier-Stokes equations in velocity-vorticity form. (English) Zbl 0895.76062
Summary: A finite difference method is presented to solve the three-dimensional Navier-Stokes equations in velocity-vorticity form. Applications of the method to flows around a cube and a sphere are realized. The comparisons between the results of the present formulation with those of the velocity-pressure formulation or with experimental data show that the method is consistent.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Keywords:
cube; sphere
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fasel, H., Untersuchungen zum problem des grenzschichtumschlages durch numerische integration der Navier-Stokes gleichungen, ()
[2] Speziale, C.G., On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics, J. computat. phys., 73, 476-480, (1987) · Zbl 0632.76049
[3] Gresho, P.M.; Sani, R.L., On pressure boundary conditions for the incompressible Navier-Stokes equations, Int. J. num. methods fluids, 7, 1111-1145, (1987) · Zbl 0644.76025
[4] Gatski, T.B., Review of incompressible fluid flow computations using the vorticity-velocity formulation, Appl. numer. math., 7, 227-239, (1991) · Zbl 0714.76033
[5] Gatski, T.B.; Grosch, C.E.; Rose, M.E., The numerical solution of the Navier-Stokes equations for 3-dimensional unsteady incompressible flows by compact schemes, J. computat. phys., 82, 298-329, (1989) · Zbl 0667.76051
[6] Huang, Y.; Ghia, U.; Osswald, G.A.; Ghia, K.N., Velocity-vorticity simulation of unsteady 3D viscous flow within a driven cavity, () · Zbl 0900.76081
[7] Osswald, G.A.; Ghia, K.N.; Ghia, U., A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations, (), 408-421 · Zbl 0683.76027
[8] Dennis, S.C.K.; Ingham, D.B.; Cook, R.N., Finite-difference methods for calculating steady incompressible flows in three dimensions, J. computat. phys., 33, 325-339, (1979) · Zbl 0421.76019
[9] Daube, O.; Guermond, J.L.; Sellier, A., Sur la formulation vitesse-tourbillon des equations de Navier-Stokes en ecoulement incompressible, C. R. acad. sci. Paris, 313, 377-382, (1991), Série II · Zbl 0735.76016
[10] Gatski, T.B.; Grosch, C.E.; Rose, M.E., A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables, J. computat. phys., 48, 1-22, (1982) · Zbl 0502.76040
[11] Orlandi, P., Vorticity-velocity formulation for high re flows, Computers & fluids, 15, 2, 137-149, (1987) · Zbl 0616.76034
[12] Guj, G.; Stella, F., Numerical solutions of high re recirculating flows in vorticity-velocity form, Int. J. num. methods fluids, 8, 405-416, (1988) · Zbl 0672.76031
[13] Daube, O., Resolution of the 2D Navier-Stokes equations in velocity-vorticity form by means of an influence matrix technique, J. computat. phys., 103, 402-414, (1992) · Zbl 0763.76046
[14] Farouk, B.; Fusegi, T., A coupled solution of the vorticity-velocity formulation of the incompressible Navier-Stokes equations, Int. J. num. methods fluids, 5, 1017-1034, (1985) · Zbl 0586.76039
[15] Stella, F.; Guj, F., Vorticity-velocity formulation in the computation of flows in multiconnected domains, Int. J. num. methods fluids, 9, 1285-1298, (1989) · Zbl 0684.76037
[16] Guj, G.; Stella, F., A vorticity-velocity method for the numerical solution of 3D incompressible flows, J. computat. phys., 106, 286-298, (1993) · Zbl 0770.76045
[17] Tromeur-Dervout, D.; Loc, T.-P., On the 3D multigrid and ADI algorithms for the numerical solution of Navier-Stokes equations on distributed memory multiprocessors, (), 473-480
[18] Toumi, A.; Loc, T.-P., Numerical study of three-dimensional viscous incompressible flow by vorticity and velocity formulation, (), 595-606
[19] Fasel, H., Investigation of the stability of boundary layers by a finite-difference model of the Navier-Stokes equations, J. fluid mech., 78, 2, 355-383, (1976) · Zbl 0404.76041
[20] Fasel, H.; Rist, U.; Konselmann, U., Numerical investigation of the three-dimentional development in boundary layer transition, () · Zbl 0850.76392
[21] Spall, R.E.; Gatski, T.B.; Ash, R.L., The structure and dynamics of bubble-type vortex breakdown, (), 613-637
[22] Labidi, W.; Loc, T.-P., Numerical resolution of the three-dimensional Navier-Stokes equations in velocity-vorticity formulation, (), 354-359
[23] Fontaine, J.; Loc, T.-P., An efficient numerical algoritm for velocity-vorticity 3D unsteady Navier-Stokes equations, (), 79-88 · Zbl 0875.76377
[24] Hasen, M.O.L., Vorticity-velocity formulation of the Navier-Stokes equations for aerodynamic flows, ()
[25] Hansen, M.O.L.; Sorensen, J.N.; Baker, V.A., A numerical investigation of 3D flow past an infinite cylinder, (), 375-382
[26] Loc, T.-P.; Labidi, W.; Dulieu, A.; Pineau, G.; Texier, A., Simulation numerique d’ecoulements instationnaires tridimensionnels par resolution des equations de Navier-Stokes sur un systeme multiprocesseur, Rapport final de synthese, convention DRET/LIMSI, no 88/047, (1990)
[27] Thibeau, S., Écoulement visqueux dans une turbomachine, ()
[28] Dennis, S.C.R.; Hudson, J.D., An h4 accurate vorticity-velocity formulation for calculating flow past a cylinder, Int. J. num. methods fluids, 21, 489-497, (1995) · Zbl 0846.76059
[29] Fontaine, J.; Loc, T.-P., Etude numérique des sillages engendrés par une plaque d’envergure finie, C. R. acad. sci. Paris, 320, 581-586, (1995), Série IIb
[30] Sagaut, P., Simulations numériques d’écoulements décollés avec des modéles de sous maille, ()
[31] Batchelor, G.K., (), 598
[32] Dennis, S.C.R.; Walker, J.D.A., Calculation of unsteady flow past a sphere at low and moderate Reynolds numbers, J. fluid. mech., 48, 771-789, (1971) · Zbl 0266.76023
[33] Rimon, Y.; Cheng, S.I., Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers, Phys. fluids, 12, 5, 949-959, (1969) · Zbl 0181.54801
[34] Schlichting, H., Boundary layer theory, (), 17
[35] Loc, T.-P.; Bouard, R., Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualisation and measurements, J. fluid mech., 160, 93-117, (1985)
[36] Jacobson, J.D., Magnus characteristics of arbitrary rotating bodies, Agardograph, 171, (1973)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.