A high-order and efficient numerical algorithm for conjugate heat transfer problems

Meng, Fanlong
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Sahni, Onkar
Banks, Jeffrey W.
Henshaw, William D.
Oberai, Assad
Zhang, Lucy T.
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Mechanical engineering
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To improve numerical schemes associated with CHT problem, we first restrict our consideration to CHT problems involving only heat transfer, as for example in solids. Then we describe a new partitioned approach for solving CHT problems where the governing temperature equations in different material domains are time-stepped in an 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.
August 2018
School of Engineering
Dept. of Mechanical, Aerospace, and Nuclear Engineering
Rensselaer Polytechnic Institute, Troy, NY
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