A rarefaction-tracking method for hyperbolic conservation laws

@article{Farjoun2010ARM,
  title={A rarefaction-tracking method for hyperbolic conservation laws},
  author={Y. Farjoun and B. Seibold},
  journal={Journal of Engineering Mathematics},
  year={2010},
  volume={66},
  pages={237-251}
}
A numerical method for scalar conservation laws in one space dimension is presented. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the… Expand

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