High-order Schemes for Viscous Hamilton-Jacobi Equations

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2005, Vol. 22 ›› Issue (2): 123-129.

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High-order Schemes for Viscous Hamilton-Jacobi Equations

CAI Li¹, FENG Jian-hu², XIE Wen-xian¹, WANG Zhen-hai¹

1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. College of Science, Chang'An University, Xi'an 710064, China

Received:2003-12-07 Revised:2004-06-27 Online:2005-03-25 Published:2005-03-25

Abstract

Abstract: Second-order and fourth-order methods for approximate solutions of viscous Hamilton-Jacobi equations are developed on the basis of the weighted essentially non-oscillator (WENO) scheme.By modifying the numerical flux,constructing the second-order approximation based on nonlinear limiter and fourth-order approximation based on Taylor expansion for viscosity term, the one- and two-dimensional viscous Hamilton-Jacobi equations are solved successfully. Numerical tests demonstrate the desired high-resolution,robustness and non-oscillatory behaviors of the schemes.

Key words: Hamilton-Jacobi equation, WENO scheme, viscosity

CLC Number:

O241
O354

CAI Li, FENG Jian-hu, XIE Wen-xian, WANG Zhen-hai. High-order Schemes for Viscous Hamilton-Jacobi Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 22(2): 123-129.

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High-order Schemes for Viscous Hamilton-Jacobi Equations

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