Premium
Analysis of explicit difference methods for a diffusion‐convection equation
Author(s) -
Siemieniuch J. L.,
Gladwell I.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620120603
Subject(s) - convection–diffusion equation , convection , numerical solution of the convection–diffusion equation , finite difference , instability , diffusion , finite difference method , mathematics , numerical analysis , numerical stability , simple (philosophy) , numerical diffusion , diffusion equation , mechanics , mathematical analysis , physics , finite element method , thermodynamics , mixed finite element method , engineering , metric (unit) , philosophy , operations management , epistemology
We consider the numerical solution of a model one‐dimensional diffusion‐convection equation by a variety of explicit finite difference methods including conventional central and upwind replacements of the convection terms. We discuss commonly observed phenomena such as instability, unwanted oscillations in the numerical solution, and numerical diffusion and we present an analysis of these effects by simple mathematical techniques.