510 IGPM510.pdf        December 2020
TITLE Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
AUTHORS Václav Kučera, Maria Lukáčová-Medvid‘ová, Sebastian Noelle, Jochen Schütz
ABSTRACT In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kuˇcera (JCP 2007) [9] as well as the class of RS-IMEX schemes [4, 17, 27, 28]. The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in [9], or a numerical approximation of the incompressible limit equations as in [30], or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.
KEYWORDS asymptotic preserving schemes, compressible Euler equations, Low-Mach limit Hilbert expansion