DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations

Date

2010-06-01

Author

Meral, Guelnihal
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

158
views

0
downloads

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 system of ordinary differential equations in time are solved using finite difference method (FDM) with a relaxation parameter and least squares method (LSM). The proposed methods are examined with numerical test problems in which the behaviours of solutions are known Although it gives almost the same accuracy with the DRBEM + FDM procedure, DRBEM + LSM solution procedure is preferred, since it is a direct method without the need of a parameter. (C) 2010 Elsevier Ltd. All rights reserved

Subject Keywords

General Engineering, Applied Mathematics, Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/47938

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

DOI

https://doi.org/10.1016/j.enganabound.2010.01.006

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

DRBEM solution of the Cauchy MHD duct flow with a slipping perturbed boundary Aydin, Cemre; Tezer, Münevver (Elsevier BV, 2018-08-01) In this study, the MHD flow direct and Cauchy problems are solved in a rectangular duct with a perturbed, curved, and slip upper boundary. The aim is to recompute the slipping velocity and the slip length by using the asymptotic analysis with respect to the perturbation parameter e and solving MHD flow equations for the first order and the corrector solutions in the rectangular duct. Hence, without discretizing the curved boundary, we are able to obtain the solution of MHD flow in the duct with curved pertu...
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...
DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations Fendoglu, Hande; Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2018-08-01) 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 treatin...
DRBEM solution of natural convection flow of nanofluids with a heat source Gumgum, S.; Tezer, Münevver (Elsevier BV, 2010-08-01) This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fractio...
Perron's theorem for linear impulsive differential equations with distributed delay Akhmet, Marat; Zafer, A. (Elsevier BV, 2006-08-15) In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable.

Citation Formats

G. Meral and M. Tezer, “DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 574–580, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47938.