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Accuracy and stability analysis of a second‐order time‐accurate loosely coupled partitioned algorithm for transient conjugate heat transfer problems
Author(s) -
KazemiKamyab V.,
Zuijlen A. H.,
Bijl H.
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3842
Subject(s) - stability (learning theory) , conjugate gradient method , algorithm , transient (computer programming) , crank–nicolson method , mathematics , coupling (piping) , numerical stability , computer science , numerical analysis , mathematical analysis , materials science , machine learning , metallurgy , operating system
SUMMARY In this paper, a second‐order time‐accurate loosely coupled partitioned algorithm is presented for solving transient thermal coupling of solids and fluids, also referred to by conjugate heat transfer. The Crank–Nicolson scheme is used for time integration. The accuracy and stability of the loosely coupled solution algorithm are analyzed analytically. Based on the accuracy analysis, the design order of the time integration scheme is preserved by following a predictor (implicit)–corrector (explicit) approach. Hence, the need to perform an additional implicit solve (a subiteration) at each time step is avoided. The analytical stability analysis shows that by using the Crank–Nicolson scheme for time integration, the partitioned algorithm is unstable for large Fourier numbers, unlike the monolithic approach. Accordingly, using the stability analysis, a stability criterion is obtained for the Crank–Nicolson scheme that imposes restriction on Δ t given the material properties and mesh spacings of the coupled domains. As the ratio of the thermal effusivities of the coupled domains reaches unity, the stability of the algorithm reduces. To demonstrate the applicability of the algorithm, a numerical example is considered (an unsteady conjugate natural convection in an enclosure). Copyright © 2013 John Wiley & Sons, Ltd.