An exact particle method for scalar conservation laws and its application to stiff reaction kinetics

@article{Farjoun2011AnEP,
  title={An exact particle method for scalar conservation laws and its application to stiff reaction kinetics},
  author={Yossi Farjoun and Benjamin Seibold},
  journal={arXiv: Numerical Analysis},
  year={2011},
  pages={105-124}
}
An “exact” method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is as accurate as the applied ODE solver. Furthermore, the method is extended to stiff balance laws. A special correction approach yields a method that evolves detonation waves at correct velocities, without resolving their internal dynamics. The particle… Expand
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