Artificial boundary method for two-dimensional Burgers' equation

Xiaonan Wu; Jiwei Zhang

doi:10.1016/j.camwa.2007.11.047

Artificial boundary method for two-dimensional Burgers' equation

Xiaonan Wu^*, Jiwei Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

17 Citations (Scopus)

Abstract

The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.

Original language	English
Pages (from-to)	242-256
Number of pages	15
Journal	Computers and Mathematics with Applications
Volume	56
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2007.11.047
Publication status	Published - Jul 2008

Scopus Subject Areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

User-Defined Keywords

Artificial boundary conditions
Dirichlet to Neumann method
Stability analysis
Two-dimensional Burgers equation
Unbounded domain

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10.1016/j.camwa.2007.11.047

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title = "Artificial boundary method for two-dimensional Burgers' equation",

abstract = "The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.",

keywords = "Artificial boundary conditions, Dirichlet to Neumann method, Stability analysis, Two-dimensional Burgers equation, Unbounded domain",

author = "Xiaonan Wu and Jiwei Zhang",

note = "Funding Information: The research is supported in part by RGC of Hong Kong and FRG of Hong Kong Baptist University. The authors would like to thank the anonymous referees for their suggestions, which led to the improvement of the paper.",

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T1 - Artificial boundary method for two-dimensional Burgers' equation

AU - Wu, Xiaonan

AU - Zhang, Jiwei

N1 - Funding Information: The research is supported in part by RGC of Hong Kong and FRG of Hong Kong Baptist University. The authors would like to thank the anonymous referees for their suggestions, which led to the improvement of the paper.

PY - 2008/7

Y1 - 2008/7

N2 - The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.

AB - The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole-Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.

KW - Artificial boundary conditions

KW - Dirichlet to Neumann method

KW - Stability analysis

KW - Two-dimensional Burgers equation

KW - Unbounded domain

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U2 - 10.1016/j.camwa.2007.11.047

DO - 10.1016/j.camwa.2007.11.047

M3 - Journal article

AN - SCOPUS:43049183609

SN - 0898-1221

VL - 56

SP - 242

EP - 256

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 1

ER -

Artificial boundary method for two-dimensional Burgers' equation

Abstract

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