DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations

Date

2018-08-01

Author

Fendoglu, Hande
Bozkaya, Canan
Tezer, Münevver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

265
views

0
downloads

The present study focuses on the numerical solution of the transient convection-diffusion-reaction equation by transforming it into modified Helmholtz equation through an exponential type transformation. In the spatial discretization of the problem domain two different boundary element methods (BEM), namely the domain BEM (DBEM) and the dual reciprocity BEM (DRBEM), are employed which are combined with an implicit backward finite difference time integration. The BEM techniques differ in the sense of treating the leftover domain integral. That is, in DBEM the domain integral is kept and calculated by quadrature while it is reduced to an equivalent boundary interal by means of radial basis functions in DRBEM. The numerical simulations are first carried out for several values of diffusion coefficient in the transient convection-diffusion-reaction equation. The results reveal that DBEM gives more accurate results for smaller values of diffusion coefficient compared to DRBEM. Thus, DBEM is further used for the solution of the coupled transient convection-diffusion type magnetohydrodynamic flow equations. The results are presented by equivelocity and current lines for various values of problem parameters, which show the well-known characteristics of the MHD flow.

Subject Keywords

General Engineering, Applied Mathematics, Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/42098

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

DOI

https://doi.org/10.1016/j.enganabound.2018.04.011

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems Bozkaya, Canan (Elsevier BV, 2007-01-01) Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Global existence and boundedness for a class of second-order nonlinear differential equations Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01) In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations Meral, Guelnihal; Tezer, Münevver (Elsevier BV, 2010-06-01) The nonlinear wave equation is solved numerically in an exterior region For the discretization of the space derivatives dual reciprocity boundary element method (DRBEM) is applied using the fundamental solution of Laplace equation. The time derivative and the nonlinearity are treated as the nonhomogenity. The boundary integrals coming from the far boundary are eliminated using rational and exponential interpolation functions which have decay properties far away from the region of Interest. The resulting sys...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Picone's formula for linear non-selfadjoint impulsive differential equations Ozbekler, A.; Zafer, Ağacık (Elsevier BV, 2006-07-15) In this paper, we derive a Picone type formula for second-order linear non-selfadjoint impulsive differential equations having fixed moments of impulse actions, and obtain a Wirtinger type inequality, a Leighton type comparison theorem, and a Sturm-Picone comparison theorem for such equations. Moreover, several oscillation criteria are also derived as applications. (c) 2005 Elsevier Inc. All rights reserved.

Citation Formats

H. Fendoglu, C. Bozkaya, and M. Tezer, “DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 124–134, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42098.