An exactly conservative particle method for one dimensional scalar conservation laws - Mathematics > Numerical AnalysisReport as inadecuate




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



Author: Yossi Farjoun, Benjamin Seibold

Source: https://arxiv.org/







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