|Preprint-No.:||< 422 >||Published in:||May 2015||PDF-File:||IGPM422.pdf|
|Title:||On the Mach-Uniformity of Lagrange-Projection Scheme|
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|