Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
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
BEM solution of unsteady convection-diffusion type fluid flow problems
Date
2020
Author
Fendoğlu, Hande
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
109
views
0
downloads
Cite This
The time-dependent convection-diffusion-reaction (CDR) type equations with constant and variable convective coefficients are solved by using two different boundary element methods (BEM), namely dual reciprocity BEM (DRBEM) and domain BEM (DBEM), in the spatial discretization while an implicit backward finite difference scheme is used in time. In the applications of DRBEM and DBEM, the fundamental solutions of both CDR equation and the modified Helmholtz (mH) equation are made use of. This results in some leftover terms (e.g. time derivative of the unknown) in the equations; and consequently some leftover domain integrals after the weighting process of the differential equations with each aforementioned fundamental solutions. The treatment of these leftover domain integrals generates different BEM formulations. That is, the DRBEM arises following the transformation of these domain integrals into equivalent boundary integrals by using radial basis functions, while keeping these domain integrals and computing them numerically, produce the DBEM. The physical applications of the present techniques are mainly on the solutions of some fluid dynamics problems which are governed by time-dependent CDR type equations. In this respect, first the time-dependent magnetohydrodynamic (MHD) flow equations which are actually convection-diffusion type equations with constant convective coefficients, are solved in ducts with straight and perturbed walls of variable electrical conductivities in the presence of an inclined magnetic field. It is found that for MHD duct flow problems, the DBEM results are almost invariant to the use of the fundamental solutions of either convection-diffusion (CD) or mH equations, while DRBEM with the fundamental solution of CD equation gives reasonably good results. Both methods capture good the well-known MHD flow characteristics for increasing values of Hartmann number. Secondly, the problems governed by Navier-Stokes and/or energy equations are considered in order to extend the application of the present method to the non-linear CD type equations with variable convective coefficients. Thus, the DBEM with the fundamental solution of CD equation is employed for the solution of the benchmark problems of fluid dynamics and heat transfer such as lid-driven cavity, natural and MHD-natural convection flow in cavities and channels. It is observed that, the obtained numerical findings are quite compatible with the physics of the fluid flow and the temperature distribution for moderate values of Reynolds, Rayleigh and Hartmann numbers.
Subject Keywords
Boundary element methods.
,
Convection-diffusion-reaction equation
,
MHD flow
,
DRBEM
,
DBEM.
URI
http://etd.lib.metu.edu.tr/upload/12625414/index.pdf
https://hdl.handle.net/11511/45481
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Solution of the nonlinear diffusion equation using the dual reciprocity boundary element method and the relaxation type time integration scheme
Meral, G (2005-03-18)
We present the combined application of the dual reciprocity boundary element method (DRBEM) and the finite difference method (FDM) with a relaxation parameter to the nonlinear diffusion equation: partial derivative u/partial derivative t = V del(2)u + p(u) at where p(u) is the nonlinear term. The DRBEM is employed to discretize the spatial partial derivatives by using the fundamental solution of the Laplace operator, keeping the time derivative and the nonlinearity as the nonhomogeneous terms in the equatio...
MUTUAL COUPLING EFFECTS OF FINITE RECTANGULAR PHASED-ARRAYS
YAVUZ, H; BUYUKDURA, OM (1994-04-14)
A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...
Hamilton-Jacobi theory of discrete, regular constrained systems
Güler, Y. (Springer Science and Business Media LLC, 1987-8)
The Hamilton-Jacobi differential equation of a discrete system with constraint equationsG α=0 is constructed making use of Carathéodory’s equivalent Lagrangian method. Introduction of Lagrange’s multipliersλ˙α as generalized velocities enables us to treat the constraint functionsG α as the generalized momenta conjugate toλ˙α. Canonical equations of motion are determined.
Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
H. Fendoğlu, “BEM solution of unsteady convection-diffusion type fluid flow problems,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Mathematics., Middle East Technical University, 2020.