Communications in Mathematical Sciences
Volume 16 (2018)
A note on the stability of implicit-explicit flux-splittings for stiff systems of hyperbolic conservation laws
Pages: 1 – 15
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 $\varepsilon$. Then, we study non-symmetric splittings. We prove that for the isentropic Euler equations, the Degond–Tang splitting [Degond & Tang, Comm. Comp. Phys., 10:1–31, 2011] and the Haack–Jin–Liu splitting [Haack, Jin Liu, Comm. Comp. Phys., 12:955–980, 2012], 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., 121:213–237, 1995], if this splitting is combined with an IMEX scheme as in [Noelle, Bispen, Arun, Lukáčová, Munz, SIAM J. Sci. Comp., 36:B989–B1024, 2014].
stiff hyperbolic systems, flux-splitting, IMEX scheme, asymptotic preserving (AP) property, modified equation, stability analysis
2010 Mathematics Subject Classification
35L65, 65M08, 76M45
The first author was supported by the scholarship of RWTH Aachen University through Graduiertenförderung nach Richtlinien zur Förderung des wissenschaftlichen Nachwuchses (RFwN).
Received 28 July 2017
Accepted 23 August 2017
Published 29 March 2018