LOW-MACH CONSISTENCY OF A CLASS OF LINEARLY IMPLICIT SCHEMES FOR THE COMPRESSIBLE EULER EQUATIONS

In this note, we give an overview of the authors' paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kucera [3] as well as the class of RS-IMEX schemes [8, 5, 1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of a discrete Hilbert expansion. The existence of the Hilbert expansion is shown under simplifying assumptions.