Premium
A comparison of time marching schemes for the transient heat conduction equation
Author(s) -
Wood W. L.,
Lewis R. W.
Publication year - 1975
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.1620090314
Subject(s) - discretization , finite element method , noise (video) , time domain , transient (computer programming) , thermal conduction , mathematics , finite difference , crank–nicolson method , heat equation , finite difference method , spacetime , crank , simple (philosophy) , algorithm , mathematical analysis , computer science , physics , geometry , quantum mechanics , artificial intelligence , cylinder , image (mathematics) , computer vision , thermodynamics , operating system , philosophy , epistemology
This paper investigates the phenomenon of ‘noise’ which is common in most time‐dependent problems. The emphasis is on the achievable accuracy that is obtained with various time‐stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.