Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10449145" target="_blank" >RIV/00216208:11320/22:10449145 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ueKX4.npEl" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ueKX4.npEl</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00211-021-01240-5" target="_blank" >10.1007/s00211-021-01240-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

Popis výsledku v původním jazyce

In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kucera (J Comput Phys 224:208-221, 2007) as well as the class of RS-IMEX schemes (Schutz 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 Kucera (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.

Název v anglickém jazyce

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

Popis výsledku anglicky

In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kucera (J Comput Phys 224:208-221, 2007) as well as the class of RS-IMEX schemes (Schutz 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 Kucera (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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptivní metody pro numerické řešení parciálních diferenciálních rovnic: analýza, odhady chyb a iterativní řešiče</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Numerische Mathematik

ISSN

0029-599X

e-ISSN

0945-3245

Svazek periodika

150

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

25

Strana od-do

79-103

Kód UT WoS článku

000721479100001

EID výsledku v databázi Scopus

2-s2.0-85119687407