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Removal of an instability in a free convection problem

Invited Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 228)

Abstract

A new computation scheme, using pressures and velocities as the principal variables, has been developed for problems in steady fluid flow and heat transfer. An instability in this scheme, due to interlinkages between the flow and energy equations, was discovered when the solution procedure was applied to the problem of buoyancy in a stably-stratified fluid. This instability was removed by devising a special underrelaxation procedure for the temperature equation.

Further computations revealed a second instability which arises when too large a perturbation is applied to a zero-flow situation.

Keywords

  • Temperature Perturbation
  • Buoyancy Term
  • Upwind Difference
  • Algebraic Reduction
  • Dimensional Boundary Layer

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6. References

  1. Caretto, L.S., R.M. Curr, and D.B. Spalding, ‘Two Numerical Methods for Three-Dimensional Boundary Layers', Submitted for Publication, (1971).

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  2. Caretto, L.S., A.D. Gosman, and D.B. Spalding, ‘Removal of an Instability in a Free Convection Problem', Imperial College Mech. Engr. Dept. Report, EF/TN/A/35 (March, 1971).

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  3. Gosman, A.D., W.M. Pun., A.K. Runchal, D.B. Spalding, and M. Wolfshtein, Heat and Mass Transfer in Recirculating Flows, Academic Press, (1969).

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  4. Gosman, A.D., and D.B. Spalding, ‘The prediction of confined three-dimensional boundary layers', Symposium on Internal Flows, University of Salford, (20–22 April 1971).

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© 1971 Springer-Verlag

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Caretto, L.S., Gosman, A.D., Spalding, D.B. (1971). Removal of an instability in a free convection problem. In: Morris, J.L. (eds) Conference on Applications of Numerical Analysis. Lecture Notes in Mathematics, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069460

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  • DOI: https://doi.org/10.1007/BFb0069460

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05656-0

  • Online ISBN: 978-3-540-36976-9

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