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Title: A stable and accurate partitioned algorithm for conjugate heat transfer

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 algorithmmore » 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.« less
Authors:
 [1] ;  [1] ;  [1] ;  [1]
  1. Rensselaer Polytechnic Inst., Troy, NY (United States)
Publication Date:
Grant/Contract Number:
AC52-07NA27344
Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 344; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Research Org:
Lawrence Livermore National Security, LLC, Livermore, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; conjugate heat transfer; optimized Schwarz method; domain decomposition; Dirichlet Neumann method; overset grids
OSTI Identifier:
1352818

Meng, F., Banks, J. W., Henshaw, W. D., and Schwendeman, D. W.. A stable and accurate partitioned algorithm for conjugate heat transfer. United States: N. p., Web. doi:10.1016/j.jcp.2017.04.052.
Meng, F., Banks, J. W., Henshaw, W. D., & Schwendeman, D. W.. A stable and accurate partitioned algorithm for conjugate heat transfer. United States. doi:10.1016/j.jcp.2017.04.052.
Meng, F., Banks, J. W., Henshaw, W. D., and Schwendeman, D. W.. 2017. "A stable and accurate partitioned algorithm for conjugate heat transfer". United States. doi:10.1016/j.jcp.2017.04.052. https://www.osti.gov/servlets/purl/1352818.
@article{osti_1352818,
title = {A stable and accurate partitioned algorithm for conjugate heat transfer},
author = {Meng, F. and Banks, J. W. and Henshaw, W. D. and Schwendeman, D. W.},
abstractNote = {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.},
doi = {10.1016/j.jcp.2017.04.052},
journal = {Journal of Computational Physics},
number = C,
volume = 344,
place = {United States},
year = {2017},
month = {4}
}