A stable and accurate partitioned algorithm for conjugate heat transfer

Journal Article · Tue Apr 25 00:00:00 EDT 2017 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2017.04.052 · OSTI ID:1352818

Meng, F. ^[1]; Banks, J. W. ^[2]; Henshaw, W. D. ^[2]; Schwendeman, D. W. ^[2]

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1. Rensselaer Polytechnic Inst., Troy, NY (United States); Rensselaer Polytechnic Institute
2. Rensselaer Polytechnic Inst., Troy, NY (United States)

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

• Research Organization: Lawrence Livermore National Security, LLC, Livermore, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1352818
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 344; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English