Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-7480
Authors: | Kučera, Václav Lukáčová-Medvid’ová, Mária Noelle, Sebastian Schütz, Jochen |
Title: | Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations |
Online publication date: | 3-Aug-2022 |
Year of first publication: | 2022 |
Language: | english |
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: | 510 Mathematik 510 Mathematics |
Institution: | Johannes Gutenberg-Universität Mainz |
Department: | FB 08 Physik, Mathematik u. Informatik |
Place: | Mainz |
ROR: | https://ror.org/023b0x485 |
DOI: | http://doi.org/10.25358/openscience-7480 |
Version: | Published version |
Publication type: | Zeitschriftenaufsatz |
License: | CC BY |
Information on rights of use: | https://creativecommons.org/licenses/by/4.0/ |
Journal: | Numerische Mathematik 150 |
Pages or article number: | 79 103 |
Publisher: | Springer |
Publisher place: | Berlin u.a. |
Issue date: | 2022 |
ISSN: | 0945-3245 |
Publisher DOI: | 10.1007/s00211-021-01240-5 |
Appears in collections: | JGU-Publikationen |
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asymptotic_properties_of_a_cl-20220729162547501.pdf | 417.04 kB | Adobe PDF | View/Open |