Mathematics – Numerical Analysis
Scientific paper
2010-01-16
Mathematics
Numerical Analysis
14 page, 7 figures, presented in the Fifth International Workshop on Meshfree Methods for Partial Differential Equations
Scientific paper
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.
Farjoun Yossi
Seibold Benjamin
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