Towards a formal theory of development/evolution and characterization of time discretized operators for heat transfer

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.

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