Autoren:	Kučera, Václav Lukáčová-Medvid’ová, Mária Noelle, Sebastian Schütz, Jochen
Titel:	Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
Online-Publikationsdatum:	3-Aug-2022
Erscheinungsdatum:	2022
Sprache des Dokuments:	Englisch
Zusammenfassung/Abstract:	In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). 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 Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), 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.
DDC-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7480
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Numerische Mathematik 150
Seitenzahl oder Artikelnummer:	79 103
Verlag:	Springer
Verlagsort:	Berlin u.a.
Erscheinungsdatum:	2022
ISSN:	0945-3245
DOI der Originalveröffentlichung:	10.1007/s00211-021-01240-5
Enthalten in den Sammlungen:	JGU-Publikationen