Skip to main content

Computation of very slow flows by the finite-difference method

  • Chapter
Very Slow Flows of Solids

Part of the book series: Mechanics of Fluids and Transport Processes ((MFTP,volume 7))

  • 162 Accesses

Abstract

The computation of steady coupled velocity and temperature fields can be done in two ways:

  1. (a)

    By computing in turn each field, i.e., by solving alternately the mechanical problem and the thermal problem. When approximate values of the nodal temperatures have been totally computed, they are used as input to solve the mechanical problem, and conversely.

  2. (b)

    By computing simultaneously both fields. This method will be considered later.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. J. Andrews: Numerical simulation of sea-floor spreading, J. Geophys. Res., 77 (1972) pp. 6470–6481.

    Article  Google Scholar 

  2. D. J. Andrews and N. H. Sleep: Numerical modelling of tectonic flow behind island arcs, Geophys. J. Roy. Astro. Soc., 38 (1974) pp. 237–251.

    Google Scholar 

  3. National Physical Laboratory: Modern computing methods, Notes on Applied Science No. 16, Her Majesty’s Stationery Office, London (1957).

    Google Scholar 

  4. W. G. Bickley: Formulae for numerical differentiation, Math. Gaz., 25 (1941) pp. 19–27.

    Article  Google Scholar 

  5. W. G. Bickley and J. C. P. Miller: Numerical differentiation near the limits of a difference table, Phil. Mag., ser. 7, 33 (1942) pp. 1–10.

    Google Scholar 

  6. J-M. Vanpé: Contribution à l’étude du manteau dans le voisinage d’une plaque de lithosphère plongeante, Thèse de 3e. cycle, Univ. de Grenoble I (1979).

    Google Scholar 

  7. F. S. Acton: Numerical methods that work, Harper & Row, New York (1970) p. 488.

    Google Scholar 

  8. J. F. Thompson, F. C. Thames and C. W. Mastin: Automatic numerical generation of body-fitted curvi-linear coordinate system for field containing any number of arbitrary 2-D bodies, J. Comput. Phys., 15 (1974) pp. 299–319.

    Article  Google Scholar 

  9. P. K. Yeung and S. C. Kot: On body-fitted coordinates for separated laminar flows past wall-mounted obstacles, Int. J. num. methods in eng., 21 (1985) pp. 929–939.

    Article  Google Scholar 

  10. R. Brepson: Numerical model of Penelope ice viscosimeter flows. In: Physics and mechanics of ice (P. Tryde, ed.), Springer Verlag, Berlin (1980) pp. 28–37.

    Google Scholar 

  11. A. Karlsson and L. Fuchs: Numerical solution of flows with viscous dissipation and fluids with a temperature-dependent viscosity. In: Numerical methods in thermal problems (R. W. Lewis, K. Morgan and B. A. Schrefler, eds.), Pineridge Press, Swansea, U.K. (1981) pp. 1024–1035.

    Google Scholar 

  12. K. V. Roberts and N. O. Weiss: Convective difference schemes, Math. Comput., 20 (1966) pp. 272–299.

    Article  Google Scholar 

  13. M. H. Houston Jr. and J-Cl. De Bremaecker: ADI solution of free-convection in a variable viscosity fluid, J. comput. Phys., 16 (1974) pp. 221–239.

    Article  Google Scholar 

  14. M. H. Houston Jr. and J-Cl. De Bremaecker: Numerical models of convection in the upper mantle, J. Geophys. Res., 80 (1975) pp. 742–751.

    Article  Google Scholar 

  15. D. R. Moore, R. S. Peckover and N. O. Weiss: Difference methods for time-dependent two-dimensional convection, Comp. Phys. Commun., 6 (1974) pp. 198–220.

    Article  Google Scholar 

  16. D. P. McKenzie, J. M. Roberts and N. O. Weiss: Convection in the mantle: towards a numerical simulation, J. fluid mech., 62 (1974) pp. 465–538.

    Article  Google Scholar 

  17. G. T. Jarvis and D. P. McKenzie: Convection in a compressible fluid with infinite Prandtl number, J. fluid mech., 96 (1980) pp. 515–583.

    Article  Google Scholar 

  18. D. R. Moore and N. O. Weiss: Two-dimensional Rayleigh-Bénard convection, J. fluid mech., 58 (1973) pp. 289–312.

    Article  Google Scholar 

  19. H. J. Stetter: Stability of nonlinear discretization algorithms. In: Numerical solution of partial differential equations (J. H. Bramble, ed.), Academic Press, New York (1966) pp. 111–123.

    Google Scholar 

  20. E. D. Waddington: Accurate modelling of glacier flow, Ph.D. Thesis, Univ. of British Columbia, Vancouver (1981).

    Google Scholar 

  21. J. C. Heinrich, P. S. Huyakorn, O. C. Zienkiewicz and A. R. Mitchell: An upwind finite element for the two-dimensional convective equation, Int. J. num. met. Eng., 11 (1977) pp. 131–143.

    Article  Google Scholar 

  22. U. Christensen: Convection with pressure-and temperature-dependent non-Newtonian rheology, Geophys. J. Roy. astron. Soc., 77 (1984) pp. 343–384.

    Google Scholar 

  23. U. Hansen and A. Ebel: Experiments with a numerical model related to mantle convection: boundary layer behaviour of small-and large-scale flows, Phys. Earth Planet. interiors, 36 (1984) pp. 374–390.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Martinus Nijhoff Publishers, Dordrecht

About this chapter

Cite this chapter

Lliboutry, L.A. (1987). Computation of very slow flows by the finite-difference method. In: Very Slow Flows of Solids. Mechanics of Fluids and Transport Processes, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3563-1_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3563-1_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8094-1

  • Online ISBN: 978-94-009-3563-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics