Time integration of three-dimensional numerical transport models
type: Item
instance of: scholarly article
title: Time integration of three-dimensional numerical transport models
zbMATH Open document ID: 0819.65122
DOI: 10.1016/0168-9274(94)00049-2
author: V. Pereyra
published in: Applied Numerical Mathematics
publication date: 1995-02-09T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/5225
review text: Several variants of the method of lines for the numerical solution of a 3D diffusion-convection equation are considered and compared, the equation being possibly nonlinear through a fall velocity of suspended material. The domain is extended to one of rectangular shape by adding dummy points. The specific methods surveyed are special second-order Runge-Kutta (necessitating stringend time step restrictions), locally one-dimensional methods (unconditionally stable, easily to vectorize and parallelize, but not accurate enough), operator splitting methods (probably the most often used type in practical applications), point and line hopscotch methods (implicit along vertical lines), and, finally, predictor-corrector methods combined with splitting. The numerical comparison includes storage needed, number of tridiagonal systems to be solved per time step, ease of vectorization and parallelization. Regretfully enough neither predictor-corrector nor operator splitting methods are considered in this part of the paper. Based on their experiments on a Cray YMP4, the authors conclude that line hopscotch is most efficient for the studied problem.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 721002
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: method of lines
zbMATH Keywords: diffusion-convection equation
zbMATH Keywords: operator splitting methods
zbMATH Keywords: hopscotch methods
zbMATH Keywords: predictor-corrector methods
zbMATH Keywords: numerical comparison
zbMATH Keywords: vectorization
zbMATH Keywords: parallelization
describes a project that uses: Hopscotch
describes a project that uses: RODAS
MaRDI profile type: Publication
OpenAlex ID: W2073589721
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description: scientific article; zbMATH DE number 721002