The dual reciprocity boundary element method solution of fluid flow problems

Download

index.pdf

Date

2010

Author

Gümgüm, Sevin

Metadata

Show full item record

Item Usage Stats

224
views

128
downloads

In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) matrices whereas all the other terms in the differential equations governing the flows are considered as nonhomogeneity. This is the main advantage of DRBEM to tackle the nonlinearities in the equations with considerably small computational cost. All the convective terms are evaluated by using the DRBEM coordinate matrix which is already computed in the formulation of nonlinear terms. The resulting systems of initial value problems with respect to time are solved with forward and central differences using relaxation parameters, and the fourth-order Runge-Kutta method. The numerical stability analysis is developed for the flow problems considered with respect to the choice of the time step, relaxation parameters and problem constants. The stability analysis is made through an eigenvalue decomposition of the final coefficient matrix in the DRBEM discretized system. It is found that the implicit central difference time integration scheme with relaxation parameter value close to one, and quite large time steps gives numerically stable solutions for all flow problems solved in the thesis. One-and-two-sided lid-driven cavity flow, natural and mixed convection flows in cavities, natural convection flow of nanofluids and micropolar fluids in enclosures are solved with several geometric configurations. The solutions are visualized in terms of streamlines, vorticity, microrotation, pressure contours, isotherms and flow vectors to simulate the flow behaviour.

Subject Keywords

Numerical analysis., Electronic computers.

URI

http://etd.lib.metu.edu.tr/upload/12611605/index.pdf
https://hdl.handle.net/11511/19500

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Numerical analysis of a projection-based stabilization method for the natural convection problems Çıbık, Aytekin Bayram; Kaya Merdan, Songül; Department of Mathematics (2011) In this thesis, we consider a projection-based stabilization method for solving buoyancy driven flows (natural convection problems). The method consists of adding global stabilization for all scales and then anti-diffusing these effects on the large scales defined by projections into appropriate function spaces. In this way, stabilization acts only on the small scales. We consider two different variations of buoyancy driven flows based on the projection-based stabilization. First, we focus on the steady-sta...
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...
Boundary element method solution of initial and boundary value problems in fluid dynamics and magnetohydrodynamics Bozkaya, Canan; Tezer, Münevver; Department of Mathematics (2008) In this thesis, the two-dimensional initial and boundary value problems invol\-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions...
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.
The comparison between the DRBEM and DQM solution of nonlinear reaction-diffusion equation MERAL, GÜLNİHAL; Tezer, Münevver (Elsevier BV, 2011-10-01) In this study, both the dual reciprocity boundary element method and the differential quadrature method are used to discretize spatially, initial and boundary value problems defined by single and system of nonlinear reaction-diffusion equations. The aim is to compare boundary only and a domain discretization method in terms of accuracy of solutions and computational cost. As the time integration scheme, the finite element method is used achieving solution in terms of time block with considerably large time ...

Citation Formats

S. Gümgüm, “The dual reciprocity boundary element method solution of fluid flow problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.