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Title: | Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations | Authors: | Kučera, Václav Lukáčová-Medvid’ová, Mária Noelle, Sebastian SCHUETZ, Jochen |
Issue Date: | 2022 | Publisher: | Source: | Numerische Mathematik, 150(1), p. 79-103 | Abstract: | In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kuˇcera (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 Kuˇcera (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. | Keywords: | 76N10;76M45;76B03;65M12 | Document URI: | http://hdl.handle.net/1942/35927 | ISSN: | 0029-599X | e-ISSN: | 0945-3245 | DOI: | 10.1007/s00211-021-01240-5 | ISI #: | 000721479100001 | Rights: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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