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

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

Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 959–980

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.120313.230813s

Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 959–980

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:   

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