Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 41, 2002 - Issue 3-4
32
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

h -ADAPTIVITY AND "HONEST" GFEM FOR ADVECTION-DOMINATED TRANSPORT

Pages 339-359 | Published online: 30 Nov 2010

References

  • Gresho , P. M. and Sani , R. L. 1998 . Incompressible Flow and the Finite Element Method , Chichester, U.K. : Wiley .
  • T. J. R. Hughes, Analysis of Transient Algorithms with Particular Reference to Stability Behaviour, in T. Belytschko and T. J. R. Hughes (eds.), Computational Methods for Transient Analysis, North-Holland, Amsterdam, 1983.
  • Hughes , T. J. R. 1987 . The Finite Element Method-Linear Static and Dynamic Finite Element Analysis , Englewood Cliffs, NJ : Prentice-Hall International .
  • Zienkiewicz , O. C. and Zhu , J. Z. 1991 . Adaptivity and Mesh Generation . Int. J. Numer. Meth. Eng. , 32 : 783 – 810 .
  • Hinton , E. and Campbell , J. S. 1974 . Local and Global Smoothing of Discontinuous Finite Element Functions Using a Least Squares Method . Int. J. Numer. Meth. Eng. , 8 : 461 – 480 .
  • Lewis , R. W. , Huang , H. C. , Usmani , A. S. and Cross , J. T. 1991 . Finite Element Analysis of Heat Transfer and Flow Problems Using Adaptive Remeshing Including Application to Solidification Problems . Int. J. Numer. Meth. Eng. , 32 : 767 – 781 .
  • P. M. Gresho, R. L. Lee, S. T. Chan, and R. L. Sani, Solution of the Time-Dependent Incompressibb Navier-Stokes and Boussinesq Equation Using the Galerkin Finite Element Method, Proc. IUTAM Symp. on Approximate Methods for Navier-Stokes Problems, Paderborn, West Germany, September 1979, pp. 203-222.
  • P. M. Gresho, R. L. Lee, and R. L. Sani, On the Time-Dependent Solution of the Incompressible Navier-Stokes Equations in Two and Three Dimensions, in Recent Advances in Numerical Methods in Fluids, vol. 1. Pineridge Press, Swansea, U.K., 1980.
  • Usmani , A. S. , Lewis , R. W. and Seetharamu , K. N. 1992 . Finite Element Modeling of Natural-Convection-Controlled Change of Phase . Int. J. Numer. Meth. Fluids , 14 : 1019 – 1036 .
  • Taylor , C. and Hood , P. 1973 . A Numerical Solution of the Navier-Stokes Equations Using the Finite Element Technique . Comput. Fluids , 1 : 73 – 100 .
  • T. J. R. Hughes, M. Mallet, and A. Mizukami, A New Finite Element Formulation for Computational Fluid Dynamics: II. Beyond SUPG. Comput. Meth. Appl. Mech. Eng., vol. 54, pp. 341-355, 1986.
  • Gresho , P. M. and Lee , R. L. 1981 . Don't Suppress the Wiggles-They Are Telling You Something! . Comput. Fluids , 9 : 223 – 253 .
  • Brooks , A. N. and Hughes , T. J. R. 1982 . Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible NavierStokes Equations . Comp. Meth. Appl. Mech. Eng. , 32 : 199 – 259 .
  • Huang , H. C. and Usmani , A. S. 1994 . Finite Element Analysis for Heat Transfer-Theory and Software , London : Springer-Verlag .
  • Usmani , A. S. 1998 . An h-Adaptive SUPG-FEM Solution of the Pure Advection Equation . Appl. Numer. Math. , 26 : 193 – 202 .
  • Usmani , A. S. 1999 . Solution of Steady and Transient Advection Problems Using an E-Adaptive Finite Element Method . Int. J. Comput. Fluid Dynam. , 11 : 249 – 259 .
  • Mayne , D. A. , Usmani , A. S. and Crapper , M. 2000 . h-Adaptive Finite Element Solution of High Rayleigh Number Thermally Driven Cavity Problem . Int. J. Numer. Meth. Heat Fluid Flow , 10 : 598 – 615 .
  • Mayne , D. A. , Usmani , A. S. and Crapper , M. 2001 . h-Adaptive Finite Element Solution of Unsteady Thermally Driven Cavity Problem . Int. J. Numer. Meth. Heat Fluid Flow , 11 : 172 – 194 .
  • A. S. Usmani, Solution of Advection Problems Using -Adaptive FEM with Discontinuity Capturing SUPG Method, Int. Symp. on Advances in Computational Heat Transfer: Book of Abstracts, Cesme, Turkey, May 1997, pp. 123-125. Organized by International Centre for Heat and Mass Transfer.
  • Leong , W. H. , Hollands , K. G. T. and Brunger , A. P. 1998 . On a Physically-Realizable Benchmark Problem in Internal Natural Convection . Int. J. Heat Mass Transfer , 41 : 3817 – 3828 .
  • Leong , W. H. , Hollands , K. G. T. and Brunger , A. P. 1999 . Experimental Nusselt Numbers for a Cubical-Cavity Benchmark Problem in Natural Convection . Int. J. Heat Mass Transfer , 42 : 1979 – 1989 .
  • H. C. Huang and A. S. Usmani, The Finite Element Analysis for Heat Transfer, SpringerVerlag, Berlin, 1994.
  • Chenoweth , D. R. and Paolucci , S. 1986 . Natural Convection in an Enclosed Vertical Air Layer with Large Horizontal Temperature Differences . J. Fluid Mech. , 169 : 173 – 210 .
  • D. A. Mayne, A. S. Usmani, and M. Crapper, h-Adaptive Finite Element Solution of Natural Convection in an Air Filled Cavity, Proc. CHT'01: Advances in Computational Heat Transfer II, Cairns, Australia, May 2001, pp. 811-818. Organized by International Centre for Heat and Mass Transfer.
  • Mayne , D. A. , Usmani , A. S. and Crapper , M. 2000 . h-Adaptive Finite Element Solution of High Rayleigh Number Thermally Driven Cavity Problem . Int. J. Numer. Meth. Heat Fluid Flow , 10 : 598 – 615 .
  • Kuyper , R. A. , Van Der Meer , Th. H. , Hoogendoorn , C. J. and Henkes , R. A. W. M. 1993 . Numerical Study of Laminar and Turbulent Natural Convection in an Inclined Square Cavity . Int. J. Heat Mass Transfer , 36 : 2899 – 2911 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.