ABSTRACT |
We analyze the stability of implicit-explicit flux-splitting schemes for stiff systems
of conservation laws. In particular, we study the modified equation of the corresponding linearized
systems. We first prove that symmetric splittings are stable, uniformly in the singular parameter
ε. Then we study non-symmetric splittings. We prove that for the barotropic Euler equations, the
Degond–Tang splitting [Degond & Tang, Comm. Comp. Phys. 10 (2011), pp. 1–31] and the Haack–
Jin–Liu splitting [Haack, Jin & Liu, Comm. Comp. Phys. 12 (2012), pp. 955 - 980], and for the shallow
water equations the recent RS-IMEX splitting are strictly stable in the sense of Majda–Pego. For the
full Euler equations, we find a small instability region for a flux splitting introduced by Klein [Klein,
J. Comp. Phys. 121 (1995), pp. 213–237], if this splitting is combined with an IMEX scheme as in
[Noelle, Bispen, Arun, Lukacova, Munz, SIAM J. Sci. Comp. 36 (2014), pp. B989–B1024]. |