TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=43049183609&partnerID=8YFLogxK
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 -