Local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems

In this article, we propose and analyse a local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems. We use the method of characteristics type to avert the difficulties caused by the nonlinear term, and use the local projection stabilized method to control spurious oscillations in the velocities due to dominant convection, and use a geometric averaging idea to decouple the monolithic problems. The stability analysis is derived and numerical tests are performed to demonstrate the robustness of this new method.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential, 2016