### 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 »

- 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}

}