Solving convection and convection-reaction problems using the method of lines
type: Item
instance of: scholarly article
title: Solving convection and convection-reaction problems using the method of lines
zbMATH Open document ID: 0857.65095
DOI: 10.1016/0168-9274(95)00118-2
author: J. M. Ware
author: M. Berzins
published in: Applied Numerical Mathematics
publication date: 1997-03-09T00:00:00Z
review text: A spatial finite volume discretization is applied to the scalar initial-boundary value problem \(u_t+f_x(x,y,u,u_x,u_y)+g_y(x,y,u,u_x,u_y)=h(x,y,u)\), where \(f\) and \(g\) are the flux functions, \(h\) is the source term. The resulting system of ordinary differential equations is solved by using operator splitting and a new linear algebra module inside the software package SPRINT2D, especially suited for very large systems of linear equations at each time step. To obtain an accurate solution, the procedure requires an effective space-time control. The method is illustrated by solving a realistic knock-modelling combustion problem in car engines.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 897531
zbMATH Keywords: convection-reaction problems
zbMATH Keywords: method of lines
zbMATH Keywords: spatial finite volume discretization
zbMATH Keywords: operator splitting
zbMATH Keywords: software package SPRINT2D
zbMATH Keywords: space-time control
zbMATH Keywords: knock-modelling combustion problem
describes a project that uses: SPRINT2D
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00118-2
OpenAlex ID: W1983930829
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description: scientific article; zbMATH DE number 897531