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

Download
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.

Suggestions

Periodic solutions and stability of differential equations with piecewise constant argument of generalized type
Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009)
In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...
Optimal Control of Diffusion Convection Reaction Equations Using Upwind Symmetric Interior Penalty Galerkin SIPG Method
Karasözen, Bülent; Yücel, Hamdullah (2012-05-01)
We discuss the numerical solution of linear quadratic optimal control problem with distributed and Robin boundary controls governed by diffusion convection reaction equations. The discretization is based on the upwind symmetric interior penalty Galerkin (SIPG) methods which lead to the same discrete scheme for the optimize-then-discretize and the discretize-then-optimize.
Inverse problems for a semilinear heat equation with memory
Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005)
In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
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.
Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations
Demir, Medine; Çıbık, Aytekin; Kaya Merdan, Songül (2022-12-15)
© 2022 Elsevier Inc.This paper considers the backward Euler based linear time filtering method for the developed energy-momentum-angular momentum conserving (EMAC) formulation of the time dependent-incompressible Navier-Stokes equations in the case of weakly enforced divergence constraint. The method adds time filtering as a post-processing step to the EMAC formulation to enhance the accuracy and to improve the approximate solutions. We show that in comparison with the Backward-Euler based EMAC formulation ...
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.