A two-grid stabilization method for solving the steady-state Navier-Stokes equations

Download

index.pdf

Date

2006-05-01

Author

Kaya Merdan, Songül

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

265
views

95
downloads

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.

Subject Keywords

Applied Mathematics, Analysis, Numerical Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/38440

Journal

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

DOI

https://doi.org/10.1002/num.20120

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows Demir, Medine (Elsevier BV, 2020-10-01) 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, includin...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
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 ...
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...
A coupled numerical scheme of dual reciprocity BEM with DQM for the transient elastodynamic problems Bozkaya, Canan (Wiley, 2008-11-12) The two-dimensional transient elastodynamic problems are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in spatial domain with the differential quadrature method (DQM) in time domain. The DRBEM with the fundamental solution of the Laplace equation transforms the domain integrals into the boundary integrals that contain the first- and the second-order time derivative terms. Thus, the application of DRBEM to elastodynamic problems results in a system of second...

Citation Formats

S. Kaya Merdan, “A two-grid stabilization method for solving the steady-state Navier-Stokes equations,” NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, pp. 728–743, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38440.