Long time stability of a linearly extrapolated blended BDF scheme for multiphysics flows

TL;DR

This paper proves the long-term stability of a blended BDF scheme for multiphysics flows like Navier-Stokes and convection problems, supported by numerical tests for large time steps.

Contribution

It introduces and proves the unconditional long time stability of a novel extrapolated blended BDF scheme for complex multiphysics flow equations.

Findings

Unconditional long time stability established for the scheme.

Numerical tests confirm stability for large time steps.

Applicable to Navier-Stokes, natural convection, and double-diffusive convection.

Abstract

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.