Stability and Convergence Analysis of a Decoupled Algorithm for a Fluid-Fluid Interaction Problem

摘要: In this paper, we analyze the stability and error estimate of a decoupled method for fluid-fluid interaction problem. This applies partitioned time stepping to decouple coupling system, which is implicit/explicit scheme was first proposed by Connors, Howell, Layton [SIAM J. Numer. Anal., 50 (2012), pp. 1297--1319]. Theoretically, prove that algorithm not only conditional stable but also long stable. We derive its convergence order $o(\Delta t+h^{\frac{3}{2}})$ velocity variables in $L^2$ norm. Besides, several numerical tests are given verify our theoretical results.