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

Date

2017-07-01

Author

AKBAŞ, MERAL
Kaya, Serap
Kaya Merdan, Songül

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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

Subject Keywords

Long time stability, Boussinesq, Magnetohydrodynamics, Navier-Stokes equations, Finite element method, BDF2 timestepping

URI

https://hdl.handle.net/11511/39892

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Test and Measurement Center In advanced Technologies (MERKEZ LABORATUVARI), Article