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An "exact" method for scalar one-dimensional hyperbolic conservation laws ispresented. The approach is based on the evolution of shock particles, separatedby local similarity solutions. The numerical solution is defined everywhere,and is as accurate as the applied ODE solver. Furthermore, the method isextended to stiff balance laws. A special correction approach yields a methodthat evolves detonation waves at correct velocities, without resolving theirinternal dynamics. The particle approach is compared to a classical finitevolume method in terms of numerical accuracy, both for conservation laws andfor an application in reaction kinetics.

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