Summary
We report on a new numerical approach based on the boundary element method to compute nonstationary incompressible Navier Stokes flows in a threedimensional container. Asymptotic error estimates are presented as well as numerical examples, in particular the secondary vortex flow in a spherical tank has been computed.
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References
BORCHERS, W.: “Eine Fourier-Spektralmethode für das Stokes-Resol-ventenproblem”, U. of Paderborn 1985, submitted, 13 pp.
BORCHERS, W., HEBEKER, F.K.: “The boundary element spectral method and applications in 3-D viscous hydrodynamics”, C.A. BREBBIA et al. (eds.), Boundary Elements VIII, Berlin 1986, 823–828.
FISCHER, T.M., ROSENBERGER, R.: “A boundary integral method for the numerical computation of the forces exerted on a sphere in viscous incompressible flows near a plane wall”, U. of Darmstadt 1985, submitted, 30 pp.
HEBEKER, F.K.: “An approximation method for the Cauchy problem to the 3-D equation of vorticity transport”, Math. Math. Appl. Sci. 5 (1983), 439–475.
HEBEKER, F.K.: “Efficient boundary element methods for 3-D viscous flows”, Numer. Meth. PDE 2 (1986), 273–297.
HEBEKER, F.K.: “Characteristics and boundary elements for three-dimensional Navier Stokes flows”, in preparation.
HEYWOOD, J.G., RANNACHER, R.: “Finite element approximation of the nonstationary Navier Stokes problem, Part I”, SIAM J. Numer. Anal. 19 (1982), 275–311.
KATO, T.: “On classical solutions of the two-dimensional nonstationary Euler equation”, Arch. Rat. Mech. Anal. 25 (1967), 188–200.
MADAY, Y., QUARTERONI, A.: “Spectral and pseudospectral approximations of the Navier Stokes equations”, SIAM J. Numer. Anal. 19 (1982), 761–780.
ORSZAG, S.A.: “Numerical simulation of incompressible flows within simple boundaries, Part I”, S.ud. Appl. Math. 2 (1971), 293–326.
PIRONNEAU, O.: “On the transport-diffusion algorithm and its applications to the Navier Stokes equations”, Numer. Math. 38 (1982), 309–332.
RAUTMANN, R.: “Ein Näherungsverfahren für spezielle parabolische Anfangswertaufgaben mit Operatoren”, Lecture Notes in Math., 267 (1972), 187–231.
TOSAKA, N., KAKUDA, K.: “Numerical simulations for incompressible viscous flow problems using the integral equation methods”, C.A. BREBBIA et al. (eds.), Boundary Elements VIII, Berlin 1986, 813–822.
VARNHORN, W.: “Zur Numerik der Gleichungen von Navier-Stokes”, PhD. thesis, U. of Paderborn 1985.
WENDLAND, W.L.: “On some mathematical aspects of boundary element methods for elliptic problems”, J.R. WHITEMAN (ed.), The Mathematics of Finite Elements and Applications V, London 1985, 193–227.
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© 1988 Springer Fachmedien Wiesbaden
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Hebeker, F.K. (1988). Characteristics and Boundary Elements for Threedimensional Nonstationary Navier Stokes Flows. In: Ballmann, J., Eppler, R., Hackbusch, W. (eds) Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics. Notes on Numerical Fluid Mechanics, vol 21. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13997-3_5
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DOI: https://doi.org/10.1007/978-3-663-13997-3_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08095-2
Online ISBN: 978-3-663-13997-3
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