The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations

E. H. Ooi; Viktor Popov

doi:10.2495/BEM130031

The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations

E. H. Ooi
, Viktor Popov

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

Abstract

In this paper, the local boundary integral equation (LBIE) method employing the simplified approach for imposing the boundary conditions is used to solve the lid driven cavity problem described by the velocity-vorticity formulations of the Navier-Stokes equations. The objective of this study is to investigate how the differentiation of the radial basis functions carried out to approximate the spatial gradients in the simplified approach affects the accuracy of the numerical solutions in problems where knowledge of the spatial gradients is of significance. The numerical results were compared with benchmark solutions and with those obtained using the radial basis integral equation method; an integral equation based meshless method that does not involve the differentiation of the RBF to approximate the spatial gradients.

Original language	English
Title of host publication	Boundary Elements and other Mesh Reduction Methods XXXV
Editors	Carlos A. Brebbia, A.H-D. Cheng
Publisher	WITPress
Pages	23-33
Number of pages	11
ISBN (Electronic)	9781845647247
ISBN (Print)	9781845647247
DOIs	https://doi.org/10.2495/BEM130031
Publication status	Published - 2013
Externally published	Yes
Event	World Conference on Boundary Elements and Other Mesh Reduction Methods 2013 - New Forest, United Kingdom Duration: 11 Jun 2013 → 13 Jun 2013 Conference number: 35th https://www.witpress.com/elibrary/wit-transactions-on-modelling-and-simulation/54 (Proceedings)

Publication series

Name	WIT Transactions on Modelling and Simulation
Volume	54
ISSN (Print)	1743-355X

Conference

Conference	World Conference on Boundary Elements and Other Mesh Reduction Methods 2013
Abbreviated title	BEM/MRM 2013
Country/Territory	United Kingdom
City	New Forest
Period	11/06/13 → 13/06/13
Internet address	https://www.witpress.com/elibrary/wit-transactions-on-modelling-and-simulation/54 (Proceedings)

Keywords

Integral equations
Meshless methods
Navier-Stokes equations
Radial basis functions
Velocity-vorticity formulation

Access to Document

10.2495/BEM130031

Cite this

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title = "The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations",

abstract = "In this paper, the local boundary integral equation (LBIE) method employing the simplified approach for imposing the boundary conditions is used to solve the lid driven cavity problem described by the velocity-vorticity formulations of the Navier-Stokes equations. The objective of this study is to investigate how the differentiation of the radial basis functions carried out to approximate the spatial gradients in the simplified approach affects the accuracy of the numerical solutions in problems where knowledge of the spatial gradients is of significance. The numerical results were compared with benchmark solutions and with those obtained using the radial basis integral equation method; an integral equation based meshless method that does not involve the differentiation of the RBF to approximate the spatial gradients.",

keywords = "Integral equations, Meshless methods, Navier-Stokes equations, Radial basis functions, Velocity-vorticity formulation",

author = "Ooi, \{E. H.\} and Viktor Popov",

note = "Copyright: Copyright 2014 Elsevier B.V., All rights reserved.; World Conference on Boundary Elements and Other Mesh Reduction Methods 2013, BEM/MRM 2013 ; Conference date: 11-06-2013 Through 13-06-2013",

year = "2013",

doi = "10.2495/BEM130031",

language = "English",

isbn = "9781845647247",

series = "WIT Transactions on Modelling and Simulation",

publisher = "WITPress",

pages = "23--33",

editor = "Brebbia, \{Carlos A.\} and A.H-D. Cheng",

booktitle = "Boundary Elements and other Mesh Reduction Methods XXXV",

url = "https://www.witpress.com/elibrary/wit-transactions-on-modelling-and-simulation/54",

}

Ooi, EH & Popov, V 2013, The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations. in CA Brebbia & AH-D Cheng (eds), Boundary Elements and other Mesh Reduction Methods XXXV. WIT Transactions on Modelling and Simulation, vol. 54, WITPress, pp. 23-33, World Conference on Boundary Elements and Other Mesh Reduction Methods 2013, New Forest, United Kingdom, 11/06/13. https://doi.org/10.2495/BEM130031

The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations. / Ooi, E. H.; Popov, Viktor.
Boundary Elements and other Mesh Reduction Methods XXXV. ed. / Carlos A. Brebbia; A.H-D. Cheng. WITPress, 2013. p. 23-33 (WIT Transactions on Modelling and Simulation; Vol. 54).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

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T1 - The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations

AU - Ooi, E. H.

AU - Popov, Viktor

N1 - Conference code: 35th

PY - 2013

Y1 - 2013

N2 - In this paper, the local boundary integral equation (LBIE) method employing the simplified approach for imposing the boundary conditions is used to solve the lid driven cavity problem described by the velocity-vorticity formulations of the Navier-Stokes equations. The objective of this study is to investigate how the differentiation of the radial basis functions carried out to approximate the spatial gradients in the simplified approach affects the accuracy of the numerical solutions in problems where knowledge of the spatial gradients is of significance. The numerical results were compared with benchmark solutions and with those obtained using the radial basis integral equation method; an integral equation based meshless method that does not involve the differentiation of the RBF to approximate the spatial gradients.

AB - In this paper, the local boundary integral equation (LBIE) method employing the simplified approach for imposing the boundary conditions is used to solve the lid driven cavity problem described by the velocity-vorticity formulations of the Navier-Stokes equations. The objective of this study is to investigate how the differentiation of the radial basis functions carried out to approximate the spatial gradients in the simplified approach affects the accuracy of the numerical solutions in problems where knowledge of the spatial gradients is of significance. The numerical results were compared with benchmark solutions and with those obtained using the radial basis integral equation method; an integral equation based meshless method that does not involve the differentiation of the RBF to approximate the spatial gradients.

KW - Integral equations

KW - Meshless methods

KW - Navier-Stokes equations

KW - Radial basis functions

KW - Velocity-vorticity formulation

UR - https://www.scopus.com/pages/publications/84887598736

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DO - 10.2495/BEM130031

M3 - Conference Paper

AN - SCOPUS:84887598736

SN - 9781845647247

T3 - WIT Transactions on Modelling and Simulation

SP - 23

EP - 33

BT - Boundary Elements and other Mesh Reduction Methods XXXV

A2 - Brebbia, Carlos A.

A2 - Cheng, A.H-D.

PB - WITPress

T2 - World Conference on Boundary Elements and Other Mesh Reduction Methods 2013

Y2 - 11 June 2013 through 13 June 2013

ER -

The influence of RBF differentiation on the accuracy of the alternative LBIE method for solving the Navier-Stokes equations

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Keywords

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