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Preprint 2008-024

An exactly conservative particle method for one dimensional scalar conservation laws

Yossi Farjoun and Benjamin Seibold

Abstract: A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.

Available as PDF (341 Kbytes).
Yossi Farjoun,
Benjamin Seibold,
Publishing information:
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; 2008-09-04.