A FDM for Burgers’ Equation on Unbounded Domains Using High-Order Artificial Boundary Conditions

Quan Zheng; Yu Feng Liu

doi:10.4028/www.scientific.net/AMM.865.233

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 865A FDM for Burgers’ Equation on Unbounded Domains...

A FDM for Burgers’ Equation on Unbounded Domains Using High-Order Artificial Boundary Conditions

Abstract:

Burgers’ equation on an unbounded domain is an important mathematical model to treat with some external problems of fluid materials. In this paper, we study a FDM of Burgers’ equation using high-order artificial boundary conditions on the unbounded domain. First, the original problem is converted into the heat equation on an unbounded domain by Hopf-Cole transformation. Thus the difficulty of nonlinearity of Burgers’ equation is overcome. Second, high-order artificial boundary conditions are given by using Padé approximation and Laplace transformation. And the conditions confine the heat equation onto a bounded computational domain. Third, we prove the solutions of the resulting heat equation and Burgers’ equation are both stable. Fourth, we establish the FDM for Burgers’ equation on the bounded computational domain. Finally, a numerical example demonstrates the stability, the effectiveness and the second-order convergence of the proposed method.

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Periodical:

Applied Mechanics and Materials (Volume 865)

Pages:

233-238

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.865.233

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Online since:

June 2017

Authors:

Quan Zheng*, Yu Feng Liu

Keywords:

Artificial Boundary Condition (ABC), Burgers’ Equation, Finite Difference Method (FDM), Hopf-Cole Transformation, Unbounded Domain

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