Continuation Methods for the Finite Element Solution of Turbulent Flow

  • D. R. Schamber
  • B. E. Larock
  • B. A. Devantier
Conference paper

Abstract

This paper concentrates on the solution of some turbulent flow problems by the combined use of the Galerkin finite element method and a continuation method; turbulence will be simulated by the k-ε model. This turbulence model is adopted here because it currently appears to represent correctly most major features of many relatively complex flows while not overburdening the user with an unduly large number of unknowns per computational node (Rodi, 1980a). Application of the finite element method to the governing equations produces a nonlinear set of algebraic equations. Obtaining solutions to these equations is the primary problem facing the investigator.

Keywords

Sedimentation Assure Pentech 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DeVantier, B.A. and B.E. Larock (1981) Sediment Transport in Stratified Turbulent Flow, Third Symposium on Turbulent Shear Flows, L.J.S. Bradbury et al., eds., University of California, Davis, Sept. 9–11, 12.12–12.17.Google Scholar
  2. Hanjalic, K. and B.E. Launder (1972) Fully Developed Asymmetric Flow in a Plane Channel, J. Fluid Mech., 5, 301–335.CrossRefGoogle Scholar
  3. Rheinboldt, W.C. (1977) Numerical Continuation Methods for Finite Element Applications, Formulations and Computational Algorithms in Finite Element Analysis: U.S.-Germany Symposium, K.J. Bathe et al., eds., August 1976, M.I.T. Press.Google Scholar
  4. Rodi, W. (1980a) Turbulence Models and Their Application in Hydraulics, State-of-the-Art Paper, IAHR.Google Scholar
  5. Rodi, W. (1980b) Turbulence Models for Environmental Problems, Prediction Methods for Turbulent Flow, von Karman Inst. Pub., McGraw-Hill, New York, 276–281.Google Scholar
  6. Schamber, D.R. and B.E. Larock (1980) Computational Aspects of Modeling Turbulent Flows by Finite Elements, Computer Methods in Fluids, K. Morgan et al., eds., Pentech Press, 339–361.Google Scholar
  7. Schamber, D.R. and B.E. Larock (1981) Numerical Analysis of Flow in Sedimentation Basins, J. Hyd. Div., ASCE, HY5, 575–591.Google Scholar
  8. Schmidt, W.R. (1978) Adaptive Step Size Selection for use with the Continuation Method, Int. J. Num. Meth. Engrg., 12, 677–694.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • D. R. Schamber
    • 1
  • B. E. Larock
    • 2
  • B. A. Devantier
    • 2
  1. 1.University of UtahUSA
  2. 2.University of CaliforniaDavisUSA

Personalised recommendations