Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations

Kučera, Václav, et al. "Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2021. 69-78. <http://eudml.org/doc/296873>.

@inProceedings{Kučera2021,
abstract = {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 Kučera [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.},
author = {Kučera, Václav, Lukáčová-Medviďová, Mária, Noelle, Sebastian, Schütz, Jochen},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {asymptotic preserving schemes; compressible Euler equations; low-Mach limit; Hilbert expansion},
location = {Prague},
pages = {69-78},
publisher = {Institute of Mathematics CAS},
title = {Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations},
url = {http://eudml.org/doc/296873},
year = {2021},
}

TY - CLSWK
AU - Kučera, Václav
AU - Lukáčová-Medviďová, Mária
AU - Noelle, Sebastian
AU - Schütz, Jochen
TI - Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2021
CY - Prague
PB - Institute of Mathematics CAS
SP - 69
EP - 78
AB - 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 Kučera [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.
KW - asymptotic preserving schemes; compressible Euler equations; low-Mach limit; Hilbert expansion
UR - http://eudml.org/doc/296873
ER -