422 RWTH Publication No: 466268        2015        IGPM422.pdf
TITLE On the Mach-Uniformity of Lagrange-Projection Scheme
AUTHORS Hamed Zakerzadeh
ABSTRACT In the present work, we show that the Lagrange–projection scheme presented in Coquel et al.’s paper (Math. of Comp. 79.271 (2010): 1493– 1533), is asymptotic preserving for isentropic Euler equations, i.e. at the dis- crete level it preserves the incompressible limit, satisfies the div-free condition as well as the asymptotic expansion for the density in the continuous level. Moreover, we prove that the scheme is positivity-preserving, L -stable and entropy-admissible under some Mach-uniform restrictions. The analysis is similar to what has been presented in the original paper, but with the emphasis on the uniformity regarding the Mach number.
KEYWORDS All-Mach number scheme, Lagrange-projection scheme, asymptotic preserving scheme, stability analysis
DOI 10.1051/m2an/2016064
Volume 51, Number 4, July-August 2017, pages 1343 - 1366