Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows
Date
2020-10-01
Author
Demir, Medine
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
352
views
0
downloads
Cite This
This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, including both energy and helicity balance of the method. We also show that the approximate solutions of the method are unconditionally stable and optimally convergent. Several numerical tests are presented for validating the support of the derived theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Subject Keywords
Applied Mathematics
,
Numerical Analysis
,
Computational Mathematics
URI
https://hdl.handle.net/11511/38867
Journal
APPLIED NUMERICAL MATHEMATICS
DOI
https://doi.org/10.1016/j.apnum.2020.04.010
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
A finite element variational multiscale method for the Navier-Stokes equations
Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky ...
A model for the computation of quantum billiards with arbitrary shapes
Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01)
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.
An Explicitly Decoupled Variational Multiscale Method for Incompressible, Non-Isothermal Flows
Belenli, Mine A.; Kaya Merdan, Songül; Rebholz, Leo G. (Walter de Gruyter GmbH, 2015-01-01)
We propose, analyze and test a fully decoupled, but still unconditionally stable and optimally accurate, variational multiscale stabilization (VMS) for incompressible, non-isothermal fluid flows. The VMS stabilization is implemented as a post-processing step, and thus can be used with existing codes. A full numerical analysis of the method is given that proves unconditional stability with respect to the timestep size, and that the method converges optimally in both time and space. Numerical tests are provid...
Fundamental solution for coupled magnetohydrodynamic flow equations
Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2007-06-01)
In this paper, a fundamental solution for the coupled convection-diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and ind...
A two-grid stabilization method for solving the steady-state Navier-Stokes equations
Kaya Merdan, Songül (Wiley, 2006-05-01)
We formulate a subgrid eddy viscosity method for solving the steady-state incompressible flow problem. The eddy viscosity does not act on the large flow structures. Optimal error estimates are obtained for velocity and pressure. The numerical illustrations agree completely with the theoretical results. (C) 2005 Wiley Periodicals, Inc.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Demir, “An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows,”
APPLIED NUMERICAL MATHEMATICS
, pp. 140–157, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38867.