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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (6): 753-771.doi: 10.3969/j.issn.1005-3085.2020.06.009

• • 上一篇    下一篇

两区域抛物方程耦合问题的二阶解耦算法（英）

闫   伟1,   单   丽2,   董春胜1   

  1. 1- 辽宁工程技术大学理学院，阜新  123000
    2- 汕头大学理学院，汕头  515063
  • 收稿日期:2018-08-20 接受日期:2019-01-09 出版日期:2020-12-15 发布日期:2021-02-15
  • 通讯作者: 单 丽 E-mail: 15241874510@163.com
  • 基金资助:
    国家自然科学基金 (11401284)；辽宁省自然科学基金 (20180551138)；国家留学基金 (201808210153).

Second-order Partitioned Time Stepping Methods for a Parabolic Two Domain Problem

YAN Wei1,   SHAN Li2,   DONG Chun-sheng1   

  1. 1- College of Science, Liaoning Technical University, Fuxin 123000\
    2- College of Science, Shantou University, Shantou 515063
  • Received:2018-08-20 Accepted:2019-01-09 Online:2020-12-15 Published:2021-02-15
  • Contact: L. Shan. E-mail address: 15241874510@163.com
  • Supported by:
    The National Natural Science Foundation of China (11401284); the Natural Science Foundation of Liaoning Province (20180551138); the China Scholarship Council (201808210153).

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摘要： 海洋与大气环流系统是通过海气交界面的相互作用而耦合在一起的，因此研究两区域两流体耦合模型的高效数值方法是非常重要的．本文针对两区域两个热传导耦合问题提出了两种二阶解耦算法．计算上，二者均实现了在每个时间层上独立求解一个热传导方程的目的，提高了计算效率，同时也简化了编程实现的难度；理论上，给出了两种方法的无条件稳定性和最优误差估计，另外数值结果也验证了理论分析结果的正确性．

关键词: 两区域抛物耦合问题, 解耦算法, 稳定性

Abstract: The atmosphere-ocean interaction can be modeled by a fluid-fluid system which coupled by some interface conditions. It is pretty important to study the robust numerical methods for the two domain coupling problem. In this paper, we study a simplified model of diffusion through two adjacent materials which are coupled across their shared interface. Two second-order partitioned time stepping schemes are proposed. Both schemes only require the solution of two decoupled parabolic problems at each time step. Hence, they are efficient in computation and can be easily implemented by using legacy codes. We also analyze their unconditional stabilities and convergence results, together with the numerical experiments, which verify our theoretical results.

Key words: parabolic two domain problem, partitioned time stepping method, stability

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