A numerical scheme with a mesh on characteristics for the Cauchy problem for one-dimensional hyperbolic conservation laws
Commun. Korean Math. Soc. 2009 Vol. 24, No. 3, 459-466
https://doi.org/10.4134/CKMS.2009.24.3.459
Printed September 1, 2009
Daeki Yoon, Hongjoong Kim, and Woonjae Hwang
Korea University
Abstract : In this paper, a numerical scheme is introduced to solve the Cauchy problem for one-dimensional hyperbolic equations. The mesh points of the proposed scheme are distributed along characteristics so that the solution on the stencil can be easily and accurately computed. This is very important in reducing errors of the scheme because many numerical errors are generated when the solution is estimated over grid points. In addition, when characteristics intersect, the proposed scheme combines corresponding grid points into one and assigns new characteristic to the point in order to improve computational efficiency. Numerical experiments on the inviscid Burgers' equation have been presented.
Keywords : conservation laws, moving mesh, non-oscillatory scheme
MSC numbers : Primary 35L65, 65M50, 65M06
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