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On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
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Date
2017-07-01
Author
AKBAŞ, MERAL
Kaya, Serap
Kaya Merdan, Songül
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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
Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
DOI
https://doi.org/10.1002/num.22061
Collections
Test and Measurement Center In advanced Technologies (MERKEZ LABORATUVARI), Article