A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems

TL;DR

This paper introduces a high-order, conditionally stable partitioned algorithm for conjugate heat transfer problems, combining summation-by-parts finite differences with SATs to ensure energy stability in complex geometries.

Contribution

The work presents a novel, provably conditionally stable partitioned scheme for CHT problems using summation-by-parts operators and SATs, with a systematic approach for stability.

Findings

The method achieves high-order accuracy in 2D CHT problems.

Stability depends on coupling parameters and SAT choices.

Numerical experiments confirm the scheme's effectiveness.

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.