A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements

Belenli, Mine; Rebholz, Leo; Tone, Florentina

doi:10.1016/j.aml.2015.01.018

A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements

Belenli M. A., Rebholz L. G., Tone F.

APPLIED MATHEMATICS LETTERS, cilt.45, ss.98-102, 2015 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 45
Basım Tarihi: 2015
Doi Numarası: 10.1016/j.aml.2015.01.018
Dergi Adı: APPLIED MATHEMATICS LETTERS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.98-102
Anahtar Kelimeler: Navier-Stokes equations, Long-time stability, Divergence-free finite elements, Crank-Nicolson, CRANK-NICOLSON, EQUATIONS, FAMILY
Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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. (C) 2015 Elsevier Ltd. All rights reserved.