Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the navier-stokes equations

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2018

Öğrenci: DUYGU VARGÜN

Danışman: SONGÜL KAYA MERDAN

Özet:

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 this stabilization scheme for spatial discretization and the linearly extrapolated BDF2 for time discretization of NSE, the fully discrete approximation of them is obtained. The existence, uniqueness, unconditional stability and convergence of the approximate solutions are proven. Also, to verify the theoretical findings, numerical experiments which indicate the efficiency of the proposed scheme are presented.