TITLE

Optimal Radial Basis Function (RBF) for Dual Reciprocity Boundary Element Method (DRBEM) applied to Coupled Burgers' Equations with Increasing Reynolds Number

AUTHOR(S)
Sayan Kaennakham; Krittidej Chanthawara; Wattana Toutip
PUB. DATE
May 2014
SOURCE
Australian Journal of Basic & Applied Sciences;May2014, Vol. 8 Issue 7, p462
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
It is well-known that high Reynolds number flows remain challenges in numerical studies. Burgers equations are ones of those considered classical test cases for testing any new numerical method. Growing as an alternative numerical techniques, Dual Reciprocity Boundary Element Method (DRBRM) has been attracting a huge amount of interest from researchers nowadays. This study has two main objectives; to investigate the performance of the Dual Reciprocity Boundary Element Method (DRBEM) when applied to couple Burgers' equations with increasing Reynolds number (Re), and to search for an optimal Radial Basis Function (RBF) for such case. Taking into consideration also the CPU time requirement for each RBF at each Re, it is found that with appropriate parameter 'c', the multiquadric type RBF has led to the most satisfactory solution when Re is increased. Moreover, all solutions obtained are in reasonably good agreement with the exact ones implying that DRBEM is able to fairly handle this type of nonlinear and couple equations when the Reynolds number.
ACCESSION #
96583898

 

Related Articles

  • The dual reciprocity boundary element method (DRBEM) with multiquadric radial basis function for coupled burgers' equations. Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana // International Journal of Multiphysics;Jun2014, Vol. 8 Issue 2, p123 

    There are three main objectives of this work; to apply the Dual Reciprocity Boundary Element Method (DRBEM) to problems under the Burgers' equations category, to search for an optimal parameter when utilizing the Multiquadric Radial Basis Function (MQRBF) and to the numerical effect on final...

  • The dual reciprocity boundary element method for two-dimensional Burgers' equations with inverse multiquadric approximation scheme. Sarboland, M.; Aminataei, A. // Journal of Concrete & Applicable Mathematics;Jan-Apr2014, Vol. 12 Issue 1/2, p102 

    The two-dimensional Burgers' equation is a mathematical model to describe various kinds of phenomena such as turbulence and viscous fluid. In this paper, the dual reciprocity boundary element method (DRBEM) is used for solving this problem. In DRBEM, the fundamental solution of the Laplace...

  • A simplified approach for imposing the boundary conditions in the local boundary integral equation method. Ooi, Ean; Popov, Viktor // Computational Mechanics;May2013, Vol. 51 Issue 5, p717 

    A simplified approach for imposing the boundary conditions in the local boundary integral equation (LBIE) method is presented. The proposed approach employs an integral equation derived using the fundamental solution and the Green's second identity when the collocation node is at the boundary of...

  • Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions. Sarboland, Maryam; Aminataei, Azim // ISRN Applied Mathematics;2012, p1 

    During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional...

  • The Meshless Local Boundary Equation Method. Honarbakhsh, B.; Tavakoli, A. // Applied Computational Electromagnetics Society Journal;Jul2013, Vol. 27 Issue 7, p550 

    A method similar to the local boundary integral equation method that preserves its properties and is free from singular integrals is proposed. The approach is based on selection of the weighting functions from a homogeneous solution of the problem rather than the fundamental solution. Many...

  • EXISTENCE OF RADIAL SOLUTIONS FOR A FOURTH ORDER PARABOLIC EQUATION. Changchun Liu; Yeshen Du // Communications in Mathematical Analysis;2008, Vol. 5 Issue 1, p44 

    We consider an initial-boundary problem for a fourth order nonlinear parabolic equation. The problem as a model arises in epitaxial growth of nanoscale thin films. Relying on some necessary uniform estimates of the approximate solutions, we prove the existence of radial symmetric solutions to...

  • Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface. Pigeonneau, Franck; Sellier, Antoine // Physics of Fluids;Sep2011, Vol. 23 Issue 9, p092102 

    We investigate numerically the axisymmetric migration of bubbles toward a free surface, using a boundary-integral technique. Our careful numerical implementation allows to study the bubble(s) deformation and film drainage; it is benchmarked against several tests. The rise of one bubble toward a...

  • Burgers' equation with high Reynolds number. Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K. // Physics of Fluids;Jun97, Vol. 9 Issue 6, p1853 

    Reports on the numerical solution of Burgers' equation involving very high Reynolds number, using an approach based on the distributed approximating functional for representing spatial derivatives of the velocity field. Difficulties in computing the numerical solution of Burgers' equation...

  • APPROXIMATE IMPLICITIZATION BASED ON RBF NETWORKS AND MQ QUASI-INTERPOLATION. Renhong Wang; Jinming Wu // Journal of Computational Mathematics;Jan2007, Vol. 25 Issue 1, p97 

    In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics