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This content will become publicly available on May 29, 2024

Title: An unconditionally energy-stable scheme for the convective heat transfer equation
Purpose This paper aims to present an unconditionally energy-stable scheme for approximating the convective heat transfer equation. Design/methodology/approach The scheme stems from the generalized positive auxiliary variable (gPAV) idea and exploits a special treatment for the convection term. The original convection term is replaced by its linear approximation plus a correction term, which is under the control of an auxiliary variable. The scheme entails the computation of two temperature fields within each time step, and the linear algebraic system resulting from the discretization involves a coefficient matrix that is updated periodically. This auxiliary variable is given by a well-defined explicit formula that guarantees the positivity of its computed value. Findings Compared with the semi-implicit scheme and the gPAV-based scheme without the treatment on the convection term, the current scheme can provide an expanded accuracy range and achieve more accurate simulations at large (or fairly large) time step sizes. Extensive numerical experiments have been presented to demonstrate the accuracy and stability performance of the scheme developed herein. Originality/value This study shows the unconditional discrete energy stability property of the current scheme, irrespective of the time step sizes.  more » « less
Award ID(s):
2012415 1522537
NSF-PAR ID:
10435217
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
International Journal of Numerical Methods for Heat & Fluid Flow
Volume:
33
Issue:
8
ISSN:
0961-5539
Page Range / eLocation ID:
2982 to 3024
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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