Finite element error analysis of a zeroth order approximate deconvolution model based on a mixed formulation

Carolina Cardoso, Manica
Kaya Merdan, Songül
A suitable discretization for the Zeroth Order Model in Large Eddy Simulation of turbulent flows is sought. This is a low order model, but its importance lies in the insight that it provides for the analysis of the higher order models actually used in practice by the pioneers Stolz and Adams [N.A. Adams, S. Stolz, On the approximate deconvolution procedure for LES, Phys. Fluids 2 (1999) 1699-1701; N.A. Adams, S. Stolz, Deconvolution methods for subgrid-scale approximation in large eddy simulation, in: B.J. Geurts (Ed.), Modem Simul. Strategies for Turbulent Flow, Edwards, Philadelphia, 2001, pp. 21-44] and others. The higher order models have proven to be of high accuracy. However, stable discretizations of them have proven to be tricky and other stabilizations, such as time relaxation and eddy viscosity, are often added. We propose a discretization based on a mixed variational formulation that gives the correct energy balance. We show it to be unconditionally stable and prove convergence.


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.
Model order reduction for nonlinear Schrodinger equation
Karasözen, Bülent; Uzunca, Murat (2015-05-01)
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reprodu...
Equivariant fields in an SU(N) gauge theory with new spontaneously generated fuzzy extra dimensions
Kürkcüoğlu, Seçkin (2016-05-11)
We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of N = 4 supersymmetric Yang-Mills theory with cubic soft supersymmetry breaking and mass deformation terms. First, we determine a particular four-dimensional fuzzy vacuum that may be expressed in terms of a direct sum of product of two fuzzy spheres, and denote it in short as S-F(2Int) x S-F(2Int) . The direct sum structure of the vacuum is clearly revealed by a suitable splitting of the scalar fields in the mode...
Analysis of stress in the elastic state in a solid cylinder subjected to periodic boundary condition
Yedekçi, Buşra; Eraslan, Ahmet Nedim; Department of Engineering Sciences (2015)
An analytical model is developed to investigate the thermoelastic response of a solid cylinder subjected to periodic boundary condition. Time dependent periodic boundary condition for the solid cylinder is treated by the help of Duhamel's theorem. The corresponding thermoelastic equation is obtained in terms of radial displacement by using basic equations of elasticity under generalized plane strain presupposition. Analytical solution of the thermoelastic equation is obtained to determine the distributions ...
ÖZALP, MÜCAHİT; Bozkaya, Canan; Türk, Önder; Department of Mathematics (2022-8-26)
In this thesis, the finite difference method (FDM) is employed to numerically solve differently defined Steklov eigenvalue problems (EVPs) that are characterized by the existence of a spectral parameter on the whole or a part of the domain boundary. The FDM approximation of the Laplace EVP is also considered due to the fact that the defining differential operator in a Steklov EVP is the Laplace operator. The fundamentals of FDM are covered and their applications on some BVPs involving Laplace operator are d...
Citation Formats
M. Carolina Cardoso and S. Kaya Merdan, “Finite element error analysis of a zeroth order approximate deconvolution model based on a mixed formulation,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 669–685, 2007, Accessed: 00, 2020. [Online]. Available: