The new numerical method for solving the system of two-dimensional Burgers' equations

Authors:
Guozhong Zhao;Xijun Yu;Rongpei Zhang
Affiliations:
Faculty of Mathematics, Baotou Teacher's College, Baotou 014030, China and Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, the system of two-dimensional Burgers' equations are solved by local discontinuous Galerkin (LDG) finite element method. The new method is based on the two-dimensional Hopf-Cole transformations, which transform the system of two-dimensional Burgers' equations into a linear heat equation. Then the linear heat equation is solved by the LDG finite element method. The numerical solution of the heat equation is used to derive the numerical solutions of Burgers' equations directly. Such a LDG method can also be used to find the numerical solution of the two-dimensional Burgers' equation by rewriting Burgers' equation as a system of the two-dimensional Burgers' equations. Three numerical examples are used to demonstrate the efficiency and accuracy of the method.