Herein, a Mach-sensitive fractional step approach is proposed for Euler-like systems. The key idea is to introduce a time-dependent splitting which dynamically decouples convection from acoustic phenomenon following the fluctuations of the flow Mach number. By doing so, one seeks to maintain the accuracy of the computed solution for all Mach number regimes. Indeed, when the Mach number takes high values, a time-explicit resolution of the overall Euler-like system is entirely performed in one of the present splitting step. On the contrary, in the low-Mach number case, convection is totally separated from the acoustic waves production. Then, by performing an appropriate correction on the acoustic step of the splitting, the numerical diffusion can be significantly reduced. A study made on both convective and acoustic subsystems of the present approach has revealed some key properties as hyperbolicity and positivity of the density and internal energy in the case of an ideal gas thermodynamics. The one-dimensional results made on a wide range of Mach numbers using an ideal and a stiffened gas thermodynamics show that the present approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.
Mots-clés : Operator splitting, fractional step, hyperbolic, low mach number flows, relaxation schemes
@article{M2AN_2018__52_1_207_0,
author = {Iampietro, D. and Daude, F. and Galon, P. and H\'erard, J.-M.},
title = {A {Mach-sensitive} splitting approach for {Euler-like} systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {207--253},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/m2an/2017063},
zbl = {1394.76075},
mrnumber = {3808159},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2017063/}
}
TY - JOUR AU - Iampietro, D. AU - Daude, F. AU - Galon, P. AU - Hérard, J.-M. TI - A Mach-sensitive splitting approach for Euler-like systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 207 EP - 253 VL - 52 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2017063/ DO - 10.1051/m2an/2017063 LA - en ID - M2AN_2018__52_1_207_0 ER -
%0 Journal Article %A Iampietro, D. %A Daude, F. %A Galon, P. %A Hérard, J.-M. %T A Mach-sensitive splitting approach for Euler-like systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 207-253 %V 52 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2017063/ %R 10.1051/m2an/2017063 %G en %F M2AN_2018__52_1_207_0
Iampietro, D.; Daude, F.; Galon, P.; Hérard, J.-M. A Mach-sensitive splitting approach for Euler-like systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 207-253. doi : 10.1051/m2an/2017063. http://archive.numdam.org/articles/10.1051/m2an/2017063/
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