A stable and high-order accurate conjugate heat transfer problem

Authors:
Jens Lindström;Jan Nordström
Affiliations:
Uppsala University, Department of Information Technology, 751 05, Uppsala, Sweden;Uppsala University, Department of Information Technology, 751 05, Uppsala, Sweden and School of Mechanical, Industrial and Aeronautical Engineering, University of the Witvatersrand, PO WITS 2050, ...
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd-, 3rd- and 4th-order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.