| Title:
|
Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations (English) |
| Author:
|
Kučera, Václav |
| Author:
|
Lukáčová-Medviďová, Mária |
| Author:
|
Noelle, Sebastian |
| Author:
|
Schütz, Jochen |
| Language:
|
English |
| Journal:
|
Programs and Algorithms of Numerical Mathematics |
| Volume:
|
Proceedings of Seminar. Hejnice, June 21-26, 2020 |
| Issue:
|
2020 |
| Year:
|
|
| Pages:
|
69-78 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note, we give an overview of the authors' paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Ku\v{c}era [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of a discrete Hilbert expansion. The existence of the Hilbert expansion is shown under simplifying assumptions. (English) |
| Keyword:
|
asymptotic preserving schemes |
| Keyword:
|
compressible Euler equations |
| Keyword:
|
low-Mach limit |
| Keyword:
|
Hilbert expansion |
| MSC:
|
65M12 |
| MSC:
|
76B03 |
| MSC:
|
76M45 |
| MSC:
|
76N10 |
| DOI:
|
10.21136/panm.2020.07 |
| . |
| Date available:
|
2021-05-05T13:40:20Z |
| Last updated:
|
2023-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703102 |
| . |
