Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
The dual reciprocity boundary element solution of helmholtz-type equations in fluid dynamics
Download
index.pdf
Date
2013
Author
Alsoy Akgün, Nagehan
Metadata
Show full item record
Item Usage Stats
307
views
288
downloads
Cite This
In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator are considered as inhomogeneity. All the inhomogeneity terms are approximated by using suitable radial basis functions, and corresponding particular solutions are derived by using the annihilator method. Transforming time dependent partial differential equations to the form of inhomogeneous modified Helmholtz equations in DRBEM application enables us to use more information from the original governing equation. These are the main original parts of the thesis. In order to obtain modified Helmholtz equation for the time dependent partial differential equations, the time derivatives are approximated at two time levels by using forward finite difference method. This also eliminates the need of another time integration scheme, and diminishes stability problems. Stream function-vorticity formulations are adopted in physical fluid dynamics problems in DRBEM by using constant elements. First, the procedure is applied to the lid-driven cavity flow and results are obtained for Reynolds number values up to 2000. The natural convection flow is solved for Rayleigh numbers between 10^3 to 10^6 when the energy equation is added to the Navier-Stokes equations. Then, double diffusive mixed convection flow problem defined in three different physical domains is solved by using the same procedure. Results are obtained for various values of Richardson and Reynolds numbers, and buoyancy ratios. Behind these, DRBEM is used for the solution of natural convection flow under a magnetic field by using two different radial basis functions for both vorticity transport and energy equations. The same problem is also solved with differential quadrature method using the form of Poisson type stream function and modified Helmholtz type vorticity and energy equations. DRBEM and DQM results are obtained for the values of Rayleigh and Hartmann numbers up to 10^6 and 300, respectively, and are compared in terms of accuracy and computational cost. Finally, DRBEM is used for the solution of inverse natural convection flow under a magnetic field using the results of direct problem for the missing boundary conditions.
Subject Keywords
Boundary element methods.
,
Fluid dynamics.
,
Navier-Stokes equations.
URI
http://etd.lib.metu.edu.tr/upload/12615729/index.pdf
https://hdl.handle.net/11511/22554
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems
Türk, Önder; Boffi, Daniele; Codina, Ramon (2016-10-01)
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two field (displacement pressure) and the three-field (stress displacement pressure) formulations. The method presented is based on a subgrid scale concept, and depends on the approximation of the unresolvable scales of the continuous solution. In general, subgrid scale techniques consist in the addition of a residual based term to the basic Galerkin formulation. The application of a stand...
DRBEM applications in fluid dynamics problems and DQM solutions of hyperbolic equations
Pekmen, Bengisen; Tezer Sezgin, Münevver; Department of Scientific Computing (2014)
In this thesis, problems of fluid dynamics defined by the two-dimensional convection-diffusion type partial differential equations (PDEs) are solved using the dual reciprocity boundary element method (DRBEM). The terms other than the Laplacian are treated as inhomogeneous terms in the DRBEM application. Once the both sides are multiplied by the fundamental solution of Laplace equation, and then integrated over the domain, all the domain integrals are transformed to boundary integrals using the Green's ident...
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 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 ...
Three dimensional laminar compressible navier stokes solver for internal rocket flow applications
Coşkun, Korhan; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2007)
A three dimensional, Navier-Stokes finite volume flow solver which uses Roe’s upwind flux differencing scheme for spatial and Runge-Kutta explicit multi-stage time stepping scheme and implicit Lower-Upper Symmetric Gauss Seidel (LU-SGS) iteration scheme for temporal discretization on unstructured and hybrid meshes is developed for steady rocket internal viscous flow applications. The spatial accuracy of the solver can be selected as first or second order. Second order accuracy is achieved by piecewise linea...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
N. Alsoy Akgün, “The dual reciprocity boundary element solution of helmholtz-type equations in fluid dynamics,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.