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Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation

Published online by Cambridge University Press:  03 June 2015

Jun Zhu and
Jianxian Qiu
Jun Zhu*
Affiliation:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China
Jianxian Qiu*
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
*
Email:zhujun@nuaa.edu.cn
Corresponding author.Email:jxqiu@xmu.edu.cn
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Abstract

In this paper, we present a new type of Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the Hamilton-Jacobi equations on the finite volume framework. The cell averages of the function and its first one (in one dimension) or two (in two dimensions) derivative values are together evolved via time approaching and used in the reconstructions. And the major advantages of the new HWENO schemes are their compactness in the spacial field, purely on the finite volume framework and only one set of small stencils is used for different type of the polynomial reconstructions. Extensive numerical tests are performed to illustrate the capability of the methodologies.

Keywords

65M0665M9935L65HWENO schemefinite volumeHamilton-Jacobi equation

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Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014, pp. 959 - 980
Copyright
Copyright © Global Science Press Limited 2014

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