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The Solution of the Boussinesq Equations by the Finite Element Method

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Numerical Simulation of Oscillatory Convection on Low-Pr Fluids

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 27))

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Summary

The solution of the time-dependent Boussinesq equations by the finite element method is studied. The primitive variables approach in combination with a so-called penalty function method is used. Elements of Crouzeix-Raviart type (continuous velocity, discontinuous pressure) are applied. The temperature-dependence is solved by a Crank-Nicolson scheme. The method is applied to the benchmark problem for oscillatory natural convection in a cavity with aspect ratio A = 4, both for the rigid-rigid (RR) case and the rigid-free (RF) case.

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References

  • C. Cuvelier, A. Segal and A.A. van Steenhoven (1986), Finite element methods and Navier-Stokes equations, Reidel Publishing Company, Dordrecht.

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  • R.L. Sani, P.M. Gresho, R.L. Lee and D.F. Griffiths (1981), The cause and the cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations, Int. J. for Num. Meth. in Fluids, Part 1: 1, pp. 17–43, Part 2: 1, pp. 171–204.

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Author information

Authors and Affiliations

  1. Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ, Delft, The Netherlands

    A. Segal, C. Cuvelier & C. Kassels

Authors
  1. A. Segal
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  2. C. Cuvelier
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  3. C. Kassels
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Editor information

Editors and Affiliations

  1. Université d’Aix-Marseille II, Marseille, France

    Bernard Roux

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© 1990 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Segal, A., Cuvelier, C., Kassels, C. (1990). The Solution of the Boussinesq Equations by the Finite Element Method. In: Roux, B. (eds) Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Notes on Numerical Fluid Mechanics (NNFM), vol 27. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87877-9_25

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  • DOI: https://doi.org/10.1007/978-3-322-87877-9_25

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07628-3

  • Online ISBN: 978-3-322-87877-9

  • eBook Packages: Springer Book Archive

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