6. Control-Volume-Based Finite-Difference and Finite-Element Methods

  1. W. J. Minkowycz3,
  2. E. M. Sparrow4 and
  3. J. Y. Murthy5
  1. B. R. Baliga1 and
  2. N. Atabaki2

Published Online: 21 JAN 2009

DOI: 10.1002/9780470172599.ch6

Handbook of Numerical Heat Transfer, Second Edition

Handbook of Numerical Heat Transfer, Second Edition

How to Cite

Baliga, B. R. and Atabaki, N. (2000) Control-Volume-Based Finite-Difference and Finite-Element Methods, in Handbook of Numerical Heat Transfer, Second Edition (eds W. J. Minkowycz, E. M. Sparrow and J. Y. Murthy), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470172599.ch6

Editor Information

  1. 3

    University of Illinois at Chicago, Department of Mechanical and Industrial Engineering (MC 251), 842 West Taylor Street, Chicago, IL 60607-7022, USA

  2. 4

    University of Minnesota-Twin Cities, Department of Mechanical Engineering, 111 Church Street, S.E., Minneapolis, MN 55455, USA

  3. 5

    Purdue University, School of Mechanical Engineering, 1288 Mechanical Engineering Building, West Lafavette, IN 47907-1288, USA

Author Information

  1. 1

    McGill University, Department of Mechanical Engineering, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6, Canada

  2. 2

    McGill University, Department of Mechanical Engineering, Heat Transfer Laboratory, 817 Sherbrooke St. W., Montral, Quebec, Canada H3A 2K6, Canada

Publication History

  1. Published Online: 21 JAN 2009
  2. Published Print: 22 DEC 2000

ISBN Information

Print ISBN: 9780471348788

Online ISBN: 9780470172599

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Keywords:

  • spectral-element methods;
  • control-volume-based finite-difference and finite-element methods (CVFDMs and CVFEMs);
  • method of weighted residuals (MWR);
  • colocated equal-order;
  • primitive variables formulation

Summary

This chapter contains sections titled:

  • Introduction

  • Governing Differential Equations

  • Domain Discretization

  • Integral Conservation Equations

  • Interpolation Functions

  • Discretized Equations for ϕ

  • Discretized Momentum Equations

  • Mass-Conserving Velocity Field and Discretized Pressure Equations

  • Boundary Treatments

  • Solution of Discretized Equations

  • Concluding Remarks

  • Acknowledgments

  • Nomenclature

  • References