### A Numerical Study of a Pathological Example of p-system.

Ph. Hoch and M. Rascle

Abstract: In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation ($\epsilon<<$1) or "relaxed" ($\epsilon$=0) schemes of Jin-Xin\cite{sx}, with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor \cite{nt}, and with higher order ENO and WENO schemes. This comparison is first made on Sod shock tube, and then on a verypathological example of a p-system constructed by Greenberg-Rascle \cite{gr}. This exotic system admits a family of periodic solutions which are shock-free but present pairs of {\it interacting centered compression waves}. Therefore, the exact solution contains big spikes. We show how these different schemes face this numerical challenge.

Paper:
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Author(s):
Ph. Hoch , <hoch@math.unice.fr>
M. Rascle , <rascle@math.unice.fr>
Publishing information:
To appear SIAM Numer. Anal.