An exact particle method for scalar conservation laws and its application to stiff reaction kinetics
Abstract
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 approach is compared to a classical finite volume method in terms of numerical accuracy, both for conservation laws and for an application in reaction kinetics.
Keywords
Cite
@article{arxiv.1001.2840,
title = {An exact particle method for scalar conservation laws and its application to stiff reaction kinetics},
author = {Yossi Farjoun and Benjamin Seibold},
journal= {arXiv preprint arXiv:1001.2840},
year = {2023}
}
Comments
14 page, 7 figures, presented in the Fifth International Workshop on Meshfree Methods for Partial Differential Equations