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

Download

index.pdf

Date

2017-07-01

Author

AKBAŞ, MERAL
Kaya, Serap
Kaya Merdan, Songül

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

274
views

117
downloads

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

Suggestions

OpenMETU
Core

A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements Belenli, Mine Akbas; Rebholz, Leo G.; Tone, Florentina (2015-07-01) We prove a long-time stability result for the finite element in space, linear extrapolated Crank-Nicolson in time discretization of the Navier-Stokes equations (NSE). From this result and a numerical experiment, we show the importance of discrete mass conservation in long-time simulations of the NSE. That is, we show that using elements that strongly enforce mass conservation can provide significantly more accurate solutions over long times, compared to those that enforce it weakly.
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions Kaya Merdan, Songül; Rebholz, Leo G. (2014-11-01) We consider a Crank-Nicolson-Adams-Bashforth temporal discretization, together with a finite element spatial discretization, for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions. We prove a restriction on the timestep that will guarantee stability, and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems.
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems Ergül, Özgür Salih (null; 2006-11-10) We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...
Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations Vargün, Duygu; Kaya Merdan, Songül; Department of Mathematics (2018) This thesis studies a projection-based variational multiscale (VMS) method based on a linearly extrapolated second order backward difference formula (BDF2) to simulate the incompressible time-dependent Navier-Stokes equations (NSE). The method concerns adding stabilization based on projection acting only on the small scales. To give a basic notion of the projection-based VMS method, a three-scale VMS method is explained. Also, the principles of the projection-based VMS stabilization are provided. By using t...

Citation Formats

M. AKBAŞ, S. Kaya, and S. Kaya Merdan, “On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems,” NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, pp. 999–1017, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39892.