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Article Dans Une Revue International Journal of Computer Mathematics Année : 2011

Spurious caustics of Dispersion Relation Preserving schemes

Pierre Sagaut
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Résumé

A linear dispersive mechanism leading to a burst in the L1 norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity and are physically associated to inter- actions between rays defined by the characteristic lines of the discrete system. This paper extends our previous work about classical schemes to dispersion-relation preserving schemes.

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Dates et versions

hal-00712744 , version 1 (28-06-2012)

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Claire David, Pierre Sagaut. Spurious caustics of Dispersion Relation Preserving schemes. International Journal of Computer Mathematics, 2011, 88 (12), pp.2625-2636. ⟨10.1080/00207160.2011.554538⟩. ⟨hal-00712744⟩
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