ISSN:
0749-159X
Keywords:
convection-reaction equations
;
Lagrangian methods
;
convective flows
;
reactive solute transport problems
;
exact finite difference schemes
;
Mathematics and Statistics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
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
Additional Material:
6 Ill.
Type of Medium:
Electronic Resource
