Li, JianHuang, PengzhanSu, JianChen, Zhangxin2019-07-072019-07-072019-07-03Boundary Value Problems. 2019 Jul 03;2019(1):115http://hdl.handle.net/1880/110598https://doi.org/10.11575/PRISM/44932Abstract In this paper, a linear, stabilized, non-spatial iterative, partitioned time stepping method is developed and studied for the nonlinear Navier–Stokes/Navier–Stokes interaction. A backward Euler scheme is utilized for the temporal discretization while a linear Oseen scheme for the trilinear term is used to affect the spatial discretization approximated by the equal order elements. Therefore, we only solve a linear Stokes problem without spatial iterative per time step for each individual domain. Then, the method exploits properties of the Navier–Stokes/Navier–Stokes system to establish the stability and convergence by rigorous analysis. Finally, numerical experiments are presented to show the performance of the proposed method.Journal Article2019-07-07enThe Author(s)https://doi.org/10.1186/s13661-019-1220-2