A Stable and High Order Interface Procedure for Conjugate Heat Transfer Problems

Abstract

This paper analyzes stability and order of accuracy of a conjugate heat transfer problem in one space dimension. The energy method is used to derive boundary and interface conditions for the continuous problem and the resulting numerical scheme is proven stable. The 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 using the Simultaneous Appriximation Term (SAT). The rate of convergence is verified using the method of manufactured solutions.