A Finite-Difference Summation-by-Parts Conditionally Stable Partitioned Algorithm for Conjugate Heat Transfer Problems

In this work, we design and analyze a novel, provably conditionally stable weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and heat equations, coupled at an interface through the continuity of temperature and heat flux. We employ high-order summation-by-parts finite-difference operators in conjunction with simultaneous-approximation-terms (SATs) in curvilinear coordinates for spatial derivatives, combined with first- and second-order time discretization, and extrapolation in time at the interface. Energy stability is maintained by carefully defining SAT parameters at the interface. A range of coupling parameters are explored to identify those that yield a stable scheme and a step-wise approach for choosing SAT parameters that result in stability is given. The effectiveness of the method is demonstrated through numerical experiments in a two-dimensional model problem on rectangular domain with curvilinear grids. The proposed approach enables the development of high-order conditionally-stable partitioned solvers suitable for general geometries.