New approach to prove the stability of a decoupled algorithm for a fluid-fluid interaction problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Zhang, Yuhong¹  Shan, Li²  Hou, Yanren^3,4 

[1] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

[2] Liaoning Tech Univ, Coll Sci, Fu Xin 123000, Peoples R China

[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[4] Xi An Jiao Tong Univ, Ctr Computat Geosci, Xian 710049, Shaanxi, Peoples R China

关键词: Fluid-fluid interaction;    Decoupled algorithm;    Stability;    Brouwer's fixed point theorem;   

DOI  :  10.1016/j.cam.2019.112695

来源: Elsevier

【 摘 要 】

The decoupled algorithm for a fluid-fluid interaction problem was first proposed by Connors et al. (2012). Compared with the study on its long time stable which was presented in Zhang et al. (2016), we adopt a new approach to prove the stability of the decoupled method on a finite time interval (0, T] herein. By using the Brouwer's fixed point theorem, the existence of the numerical solution is proved. At the same time, by considering the error estimate between the exact solution and the numerical solution, we derive the stability of the decoupled method under the condition of Delta t + h <= c from the inductive method. Furthermore, we prove the uniqueness of the numerical solution when Delta t is appropriately small. The main theoretical results about the decoupled algorithm in this paper are new. (C) 2019 Elsevier B.V. All rights reserved.

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