CONNORS J M,HOWELL J S,LAYTON W J.Decoupled time stepping methods for fluid-fluid interaction[J].SIAM J Numer Anal,2012,50(3):1297-1319.

BRESCH D,KOKO J.Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids[J].Int J Appl Math Comput Sci,2006,16(4):419-429.

LI J,HUANG P Z,SU J,et al.A linear,stabilized,non-spatial iterative,partitioned time stepping method for the nonlinear Navier-Stokes/Navier-Stokes interaction model[J].Bound Value Probl,2019,2019:1-19.

LI J,HUANG P Z,ZHANG C,et al.A linear,decoupled fractional time-stepping method for the nonlinear fluid-fluid interaction[J].Numer Methods Part Differ Equ,2019,35(5):1873-1889.

LI W,HUANG P Z.A two-step decoupled finite element algorithm for a nonlinear fluid-fluid interaction problem[J].Univ Politeh Buchar Sci Bull Ser A Appl Math Phys,2019,81(4):107-118.

LI W,HUANG P Z,HE Y N.Grad-div stabilized finite element schemes for the fluid-fluid interaction model[J].Commun Comput Phys,2021,30(2):536-566.

李伟,黄鹏展.流体相互作用模型的粘性分离有限元方法[J].数学物理学报,2020,40(5):1362-1380.

ZHANG Y H,HOU Y R,SHAN L.Stability and convergence analysis of a decoupled algorithm for a fluid-fluid interaction problem[J].SIAM J Numer Anal,2016,54(5):2833-2867.

王小娟,贾宏恩.不可压缩的Brinkman-Forchheimer方程的回溯两重网格法[J].新疆大学学报(自然科学版)(中英文),2021,38(3):275-284.

SHEN J,XU J.Convergence and error analysis for the scalar auxiliary variable(SAV) schemes to gradient flows[J].SIAM J Numer Anal,2018,56(5):2895-2912.

AGGUL M,EROGLU F,KAYA S,et al.A projection based variational multiscale method for a fluid-fluid interaction problem[J].Comput Methods Appl Mech Engrg,2020,365(15):112957.