Artificial boundary method for two-dimensional Burgers' equation

Xiaonan WU*, Jiwei Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

17 Citations (Scopus)


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 languageEnglish
Pages (from-to)242-256
Number of pages15
JournalComputers and Mathematics with Applications
Issue number1
Publication statusPublished - 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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