A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917283796877312 |
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| author | Nataj, Sarah Fernández, David C. Del Rey Brown, David Jaiman, Rajeev |
| author_facet | Nataj, Sarah Fernández, David C. Del Rey Brown, David Jaiman, Rajeev |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_17843 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems Nataj, Sarah Fernández, David C. Del Rey Brown, David Jaiman, Rajeev Numerical Analysis 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. |
| title | A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.17843 |