On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems

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AKBAŞ M., KAYA S., Rebholz L. G.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.33, no.4, pp.999-1017, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1002/num.22061
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.999-1017
  • Keywords: Long time stability, Boussinesq, Magnetohydrodynamics, Navier-Stokes equations, finite element method, BDF2 timestepping, NAVIER-STOKES EQUATIONS, IMPLICIT EULER SCHEME, CRANK-NICOLSON, EFFICIENT, SYSTEM
  • Middle East Technical University Affiliated: Yes

Abstract

We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolson scheme for NSE, and find that BDF2LE has better stability properties, particularly for smaller viscosity values. (c) 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 999-1017, 2017