  This paper investigates the long time stability behavior of multiphysics flow
problems, namely the Navier-Stokes equations, natural convection and
double-diffusive convection equations with an extrapolated blended BDF
time-stepping scheme. This scheme combines the two-step BDF and three-step BDF
time stepping schemes. We prove unconditional long time stability theorems for
each of flow systems. Various numerical tests are given for large time step
sizes in long time intervals in order to support theoretical results.
