### A FINITE VOLUME METHOD PRESERVING MAXIMUM PRINCIPLE FOR THE CONJUGATE HEAT TRANSFER PROBLEMS WITH GENERAL INTERFACE CONDITIONS

Huifang Zhou1,2, Zhiqiang Sheng3,4, Guangwei Yuan3

1. 1. School of Mathematics, Jilin University, Changchun 130012, China;
2. The Graduate School of China Academy of Engineering Physics, Beijing 100088, China;
3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
4. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
• Received:2020-10-04 Revised:2021-03-05 Published:2023-03-14
• Contact: Guangwei Yuan, Email:yuan_guangwei@iapcm.ac.cn
• Supported by:
This work is partially supported by the National Natural Science Foundation of China (11971069,12071045), and the Foundation of CAEP (CX20210042), and Science Challenge Project (No. TZ2016002).

Huifang Zhou, Zhiqiang Sheng, Guangwei Yuan. A FINITE VOLUME METHOD PRESERVING MAXIMUM PRINCIPLE FOR THE CONJUGATE HEAT TRANSFER PROBLEMS WITH GENERAL INTERFACE CONDITIONS[J]. Journal of Computational Mathematics, 2023, 41(3): 345-369.

In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in  increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in . The accuracy and DMP-preserving property of the scheme are also verified in the numerical experiments.

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