Solution to transient Navier-Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method

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 equation, which links stream function and vorticity with an initial vorticity guess, produces velocity components in turn for the solution to vorticity transport equation. The DRBEM formulation of the vorticity transport equation results in an initial value problem represented by a system of first-order ordinary differential equations in time. When the DQM discretizes this system in time direction, we obtain a system of linear algebraic equations, which gives the solution vector for vorticity at any required time level. The procedure outlined here is also applied to solve the problem of two-dimensional natural convection in a cavity by utilizing an iteration among the stream function, the vorticity transport and the energy equations as well. The test problems include two-dimensional flow in a cavity when a force is present, the lid-driven cavity and the natural convection in a square cavity. The numerical results are visualized in terms of stream function, vorticity and temperature contours for several values of Reynolds (Re) and Rayleigh (Ra) numbers. Copyright (C) 2008 John Wiley & Sons, Ltd.


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...
Two-level finite element method with a stabilizing subgrid for the incompressible Navier-Stokes equations
NESLİTÜRK, ALİ İHSAN; Aydın Bayram, Selma; Tezer, Münevver (Wiley, 2008-10-20)
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 ...
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...
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...
Differential quadrature solution of nonlinear reaction-diffusion equation with relaxation-type time integration
Meral, G.; Tezer, Münevver (Informa UK Limited, 2009-01-01)
This paper presents the combined application of differential quadrature method (DQM) and finite-difference method (FDM) with a relaxation parameter to nonlinear reaction-diffusion equation in one and two dimensions. The polynomial-based DQM is employed to discretize the spatial partial derivatives by using Gauss-Chebyshev-Lobatto points. The resulting system of ordinary differential equations is solved, discretizating the time derivative by an explicit FDM. A relaxation parameter is used to position the sol...
Citation Formats
C. Bozkaya and M. Tezer, “Solution to transient Navier-Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 215–234, 2009, Accessed: 00, 2020. [Online]. Available: