Nonstandard methods for the convective transport equation with nonlinear reactions

  1. Hristo V. Kojouharov,
  2. Benito M. Chen*

Article first published online: 7 DEC 1998

DOI: 10.1002/(SICI)1098-2426(199807)14:4<467::AID-NUM3>3.0.CO;2-I

Issue

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations

Volume 14, Issue 4, pages 467–485, July 1998

Additional Information

How to Cite

Kojouharov, H. V. and Chen, B. M. (1998), Nonstandard methods for the convective transport equation with nonlinear reactions. Numerical Methods for Partial Differential Equations, 14: 467–485. doi: 10.1002/(SICI)1098-2426(199807)14:4<467::AID-NUM3>3.0.CO;2-I

Author Information

  1. Department of Mathematics, University of Wyoming, P.O. Box 3036, Laramie, Wyoming 82071

*Department of Mathematics, University of Wyoming, P.O. Box 3036, Laramie, Wyoming 82071

Publication History

  1. Issue published online: 7 DEC 1998
  2. Article first published online: 7 DEC 1998
  3. Manuscript Accepted: 23 JAN 1998
  4. Manuscript Received: 3 JUN 1997

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Keywords:

  • convection-reaction equations;
  • Lagrangian methods;
  • convective flows;
  • reactive solute transport problems;
  • exact finite difference schemes

Abstract

A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467–485, 1998

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