Numerical simulation of Camassa-Holm peakons by adaptive upwinding

Authors:
Robert Artebrant;Hans Joachim Schroll
Affiliations:
Centre for Mathematical Sciences, Lund University, Lund, Sweden;Centre for Mathematical Sciences, Lund University, Lund, Sweden
Venue:
Applied Numerical Mathematics
Year:
2006

Citing 6
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Abstract

The Camassa-Holm equation is a conservation law with a non-local flux that models shallow water waves and features soliton solutions with a corner at their crests, so-called peakons. In the present paper a finite-volume method is developed to simulate the dynamics of peakons. This conservative scheme is adaptive, high resolution and stable without any explicit introduction of artificial viscosity. A numerical simulation indicates that a certain plateau shaped travelling wave solution breaks up in time.