Premium
Numerical analysis of two‐level finite difference schemes for unsteady diffusion–convection problems
Author(s) -
Rigal Alain
Publication year - 1989
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.1620280503
Subject(s) - mathematics , numerical analysis , diffusion , dissipation , numerical stability , convection–diffusion equation , finite difference , convection , stability (learning theory) , finite difference method , numerical diffusion , finite difference scheme , fourier analysis , von neumann stability analysis , mathematical analysis , fourier transform , mechanics , physics , computer science , machine learning , thermodynamics
This paper develops, for linear diffusion–convection model problems, the numerical analysis of some two‐time‐level second order finite difference schemes: modified centred, upstream weighted, Samarskii explicit and implicit schemes. The stability and related properties—dissipation, amplitude and phase errors, numerical diffusion and dispersion—are studied through Fourier analysis. The behaviour of the numerical solution is analysed from the matrix properties of the schemes with special emphasis on parabolicity and positivity. These analyses allow a comparison of the properties of every scheme, the main criterion being the efficiency of the scheme for strongly convective problems.