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    A rarefaction-tracking method for hyperbolic conservation laws

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    Genre
    Journal Article
    Date
    2010-01-01
    Author
    Farjoun, Y
    Seibold, B
    Subject
    Method of characteristics
    Network flow
    Particle method
    Reaction kinetics
    Similarity solution
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6066
    
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    DOI
    10.1007/s10665-009-9338-3
    Abstract
    A numerical method for scalar conservation laws in one space dimension is presented. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing; nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. Numerical examples are presented, and specific applications and extensions of the approach outlined. © Springer Science+Business Media B.V. 2009.
    Citation to related work
    Springer Science and Business Media LLC
    Has part
    Journal of Engineering Mathematics
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/6048
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