Error estimates of a decoupled algorithm for a fluid-fluid interaction problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:333

Article

Zhang, Yuhong^1,2  Hou, Yanren^2,3  Shan, Li⁴ 

[1] Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China

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

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

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

关键词: Fluid-fluid interaction;    Decoupled algorithm;    Error estimates;   

DOI  :  10.1016/j.cam.2017.10.039

来源: Elsevier

【 摘 要 】

In this paper, we study the error estimates of a decoupled algorithm for the fluid-fluid model. The system consists of two Navier-Stokes equations which are coupled by a set of linear interface conditions. We apply the partitioned time stepping method to decouple the system. The corresponding scheme is unconditionally stable and we prove that the error estimates for velocities in L-2 norm are optimal. Moreover, under a restriction on the time step scale, we prove that the. convergent orders for the velocities in H-1 norm and for the pressures in L-2 norm are Delta t(7/8) + h and Delta t(3/4) + h, respectively. Two numerical examples are given to verify our theoretical results. Besides, by comparing the decoupled algorithm with the coupled one, numerical test shows the effectiveness of our decoupled method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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