TY - JOUR
T1 - Towards a formal theory of development/evolution and characterization of time discretized operators for heat transfer
AU - Tamma, Kumar K.
AU - Zhou, Xiangmin
AU - Sha, Desong
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
KW - Discretized operators
KW - Heat transfer
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U2 - 10.1108/09615539910260185
DO - 10.1108/09615539910260185
M3 - Article
AN - SCOPUS:0000450409
SN - 0961-5539
VL - 9
SP - 348
EP - 380
JO - International Journal of Numerical Methods for Heat and Fluid Flow
JF - International Journal of Numerical Methods for Heat and Fluid Flow
IS - 3
ER -