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

• DOI: 10.1016/j.cam.2017.10.039
• Publication Date: 2017-11-16T20:46:29Z
• Authors: Yuhong Zhang; Yanren Hou; Li Shan
• Keywords: 0101 mathematics; 01 natural sciences

Abstract 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 Δ t 7 8 + h and Δ 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.