Summary
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.
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Acknowledgments
The authors would like to acknowledge the support by the National Science Foundation. Y. Farjoun was supported by NSF grant DMS–0703937, and by the Spanish Ministry of Science and Innovation under grant FIS2008-04921–C02–01. B. Seibold was partially supported by NSF grant DMS–0813648.
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Farjoun, Y., Seibold, B. (2011). An exact particle method for scalar conservation laws and its application to stiff reaction kinetics. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations V. Lecture Notes in Computational Science and Engineering, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16229-9_7
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DOI: https://doi.org/10.1007/978-3-642-16229-9_7
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