A numerical study of a pathologicalexample of p - systemPh
نویسندگان
چکیده
In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation (<<1) or "relaxed" (=0) schemes of Jin-Xin 4], with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor 6], and with higher order ENO and WENO schemes. This comparison is rst made on Sod shock tube, and then on a very pathological example of a p-system constructed by Greenberg-Rascle 1]. This exotic system admits a family of periodic solutions which are shock-free but present pairs of interacting centered compression waves. Therefore, the exact solution contains big spikes. We show how these diierent schemes face this numerical challenge.
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