Long time stability of a linearly extrapolated blended BDF scheme for multiphysics flows
Provides theoretical stability guarantees for a practical time-stepping scheme in multiphysics simulations, but the method is an incremental combination of existing BDF schemes.
The paper proves unconditional long time stability for multiphysics flows (Navier-Stokes, natural convection, double-diffusive convection) using a blended BDF scheme, supported by numerical tests with large time steps over long intervals.
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.