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

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2018
Vargün, Duygu
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.

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Citation Formats
D. Vargün, “Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations,” M.S. - Master of Science, Middle East Technical University, 2018.