A generalized 1-dimensional particle transport method for convection diffusion reaction model
type: Item
instance of: scholarly article
title: A generalized 1-dimensional particle transport method for convection diffusion reaction model
zbMATH Open document ID: 1259.82105
author: James Makungu
author: Heikki Haario
author: William Charles Mahera
published in: Afrika Matematika
publication date: 2013-01-09T00:00:00Z
review text: The present paper develops a method for the numerical solution of convection-diffusion-reaction problems. As the authors state in the abstract, ``the technique is based on the unifying Eulerian-Lagrangian schemes (particle transport method) under the framework of operator splitting method''. In the paper, at any time interval first the convection-reaction subproblem is solved neglecting the diffusion coefficient. The solution of the convection-reaction problem, transformed onto a grid system, serves then as initial condition of the solution of the diffusion problem. Additionally, two boundary conditions have to be taken into account. It is assumed that the effects of convection and diffusion may be of the same order of magnitude. Besides, the model may change from a parabolic-type to a hyperbolic-type problem in dependence on the dominance of diffusion or convection. Results for non-stiff and stiff chemical reactions are found. For non-stiff reactions solutions are obtained for three-component systems. In this case, for every time step the results by particle transport method technique and the method of lines are compared. Concerning the stiff reactions, an ozone model of the Earth's atmosphere with time-dependent rate constants is considered. Here, numerically possible oscillations of the solution have been excluded applying adaptivity and projection techniques. Again, solutions by particle transport method technique and the method of lines are compared. It is found that the particle transport method is rather useful in cases with steep particle fronts, but it is much more time consuming than the method of lines.
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 76M28
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 76R05
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 6123650
zbMATH Keywords: transport theory
zbMATH Keywords: convection-diffusion-reaction models
zbMATH Keywords: operator splitting
zbMATH Keywords: method of lines
zbMATH Keywords: particle transport method
reviewed by: Claudia-Veronika Meister
MaRDI profile type: Publication
full work available at URL: s13370-011-0007-0
OpenAlex ID: W2042096429
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DOI: 10.1007/S13370-011-0007-0
description: scientific article; zbMATH DE number 6123650