Towards a formal theory of development/evolution and characterization of time discretized operators for heat transfer
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 May 1999
Abstract
The time‐discretization process of transient equation systems is an important concern in computational heat transfer applications. As such, the present paper describes a formal basis towards providing the theoretical concepts, evolution and development, and characterization of a wide class of time discretized operators for transient heat transfer computations. Therein, emanating from a common family tree and explained via a generalized time weighted philosophy, the paper addresses the development and evolution of time integral operators [IO], and leading to integration operators [InO] in time encompassing single‐step integration operators [SSInO], multi‐step integration operators [MSInO], and a class of finite element in time integration operators [FETInO] including the relationships and the resulting consequences. Also depicted are those termed as discrete numerically assigned [DNA] algorithmic markers essentially comprising of both: the weighted time fields, and the corresponding conditions imposed upon the dependent variable approximation, to uniquely characterize a wide class of transient algorithms. Thereby, providing a plausible standardized formal ideology when referring to and/or relating time discretized operators applicable to transient heat transfer computations.
Keywords
Citation
Tamma, K.K., Zhou, X. and Sha, D. (1999), "Towards a formal theory of development/evolution and characterization of time discretized operators for heat transfer", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 9 No. 3, pp. 348-381. https://doi.org/10.1108/09615539910260185
Publisher
:MCB UP Ltd
Copyright © 1999, MCB UP Limited