# Two-level finite element method with a stabilizing subgrid for the incompressible Navier-Stokes equations

2008-10-20
NESLİTÜRK, ALİ İHSAN
Aydın Bayram, Selma
Tezer, Münevver
We consider the Galerkin finite element method for the incompressible Navier-Stokes equations in two dimensions. The domain is discretized into a set of regular triangular elements and the finite-dimensional spaces emploved consist of piecewise continuous linear interpolants enriched with the residual-free bubble functions. To find the bubble part of the Solution, a two-level finite element method with a stabilizing subgrid of a single node is described, and its application to the Navier-Stokes equation is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems. The results show that the proper choice of the subgrid node is crucial in obtaining stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Copyright (C) 2008 John Wiley & Sons, Ltd.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

# Suggestions

 Effects of the Jacobian evaluation on Newton's solution of the Euler equations Onur, O; Eyi, Sinan (Wiley, 2005-09-20) Newton's method is developed for solving the 2-D Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes. Both analytical and numerical methods are used for Jacobian calculations. Although the numerical method has the advantage of keeping the Jacobian consistent with the numerical residual vector and avoiding extremely complex analytical differentiations, it may have accuracy problems and need longer execution time. In order to improve the accurac...
 Time-domain BEM solution of convection-diffusion-type MHD equations Bozkaya, N.; Tezer, Münevver (Wiley, 2008-04-20) The two-dimensional convection-diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state it...
 Solution to transient Navier-Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method Bozkaya, Canan; Tezer, Münevver (Wiley, 2009-01-20) The two-dimensional time-dependent Navier-Stokes equations in terms of the vorticity and the stream function are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in space with the differential quadrature method (DQM) in time. In DRBEM application, the convective and the time derivative terms in the vorticity transport equation are considered as the nonhomogeneity in the equation and are approximated by radial basis functions. The solution to the Poisson equati...
 The DRBEM solution of incompressible MHD flow equations Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10) This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
 The finite element method for MHD flow at high Hartmann numbers Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2005-01-01) A stabilized finite element method using the residual-free bubble functions (RFB) is proposed for solving the governing equations of steady magnetohydrodynamic duct flow. A distinguished feature of the RFB method is the resolving capability of high gradients near the layer rep-ions without refining mesh. We show that the RFB method is stable by proving that the numerical method is coercive even not only at low values but also at moderate and high values of the Hartmann number. Numerical results confirming t...
Citation Formats
A. İ. NESLİTÜRK, S. Aydın Bayram, and M. Tezer, “Two-level finite element method with a stabilizing subgrid for the incompressible Navier-Stokes equations,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 551–572, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35979. 