A NUMERICAL STUDY OF A PATHOLOGICAL EXAMPLE OF p-SYSTEM∗
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 and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 235–277] with the second-order Lax–Friedrichs scheme of Nessyahu and Tadmor [J. Comp. Phys., 87 (1990), pp. 408–463] and with higher-order essentially nonoscillatory (ENO) and weighted essentially nonoscillatory (WENO) schemes. This comparison is made first on a Sod shock tube and then on a very pathological example of a psystem constructed by Greenberg and Rascle [Arch. Ration. Mech. Anal., 115 (1991), pp. 395–407]. 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 different schemes face this numerical challenge.
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