POD-ROM for the Darcy-Brinkman equations with double-diffusive convection

Date

2019-09-01

Author

Eroglu, Fatma G.
Kaya Merdan, Songül
Rebholz, Leo G.

Metadata

Show full item record

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

Item Usage Stats

166
views

0
downloads

This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced model based on proper orthogonal decomposition, present a stability and convergence analyses for it, and give results for numerical tests on a benchmark problem which show it is an effective approach to model reduction in this setting.

Subject Keywords

Computational Mathematics

URI

https://hdl.handle.net/11511/37762

Journal

JOURNAL OF NUMERICAL MATHEMATICS

DOI

https://doi.org/10.1515/jnma-2017-0122

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

DRBEM solution to MHD flow in ducts with thin slipping side walls and separated by conducting thick Hartmann walls Senel, P.; Tezer-Sezgin, M. (Elsevier BV, 2019-11-01) In this study, the dual reciprocity boundary element method (DRBEM) solution to magnetohydrodynamic (MHD) flow is given in a single and two ducts stacked in the direction of external magnetic field. The duct walls perpendicular to the applied magnetic field (Hartmann walls) are conducting, thick and no-slip whereas the horizontal walls (side walls) are insulated, thin and allow the velocity slip. The DRBEM transforms the convection diffusion type MHD equations in the duct and Laplace equation in the thick w...
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 ...
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...
Perron's theorem for linear impulsive differential equations with distributed delay Akhmet, Marat; Zafer, A. (Elsevier BV, 2006-08-15) In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable.
DRBEM solution of the Cauchy MHD duct flow with a slipping perturbed boundary Aydin, Cemre; Tezer, Münevver (Elsevier BV, 2018-08-01) In this study, the MHD flow direct and Cauchy problems are solved in a rectangular duct with a perturbed, curved, and slip upper boundary. The aim is to recompute the slipping velocity and the slip length by using the asymptotic analysis with respect to the perturbation parameter e and solving MHD flow equations for the first order and the corrector solutions in the rectangular duct. Hence, without discretizing the curved boundary, we are able to obtain the solution of MHD flow in the duct with curved pertu...

Citation Formats

F. G. Eroglu, S. Kaya Merdan, and L. G. Rebholz, “POD-ROM for the Darcy-Brinkman equations with double-diffusive convection,” JOURNAL OF NUMERICAL MATHEMATICS, pp. 123–139, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37762.