A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems
Abstract
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 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 discretizations and temporal extrapolation at the interface. Energy stability is maintained by carefully selecting SAT parameters at the interface. A range of coupling parameters are explored to identify those that yield a stable scheme, and a stepwise approach for choosing SAT parameters that ensure stability is given. The effectiveness of the method is demonstrated through numerical experiments in a two-dimensional model problem on a rectangular domain with curvilinear grids. The proposed approach enables the development of high-order, conditionally stable partitioned solvers suitable for general geometries.
Cite
@article{arxiv.2602.17843,
title = {A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems},
author = {Sarah Nataj and David C. Del Rey Fernández and David Brown and Rajeev Jaiman},
journal= {arXiv preprint arXiv:2602.17843},
year = {2026}
}