Volume 52, Number 1, January–February 2018
|Page(s)||207 - 253|
|Published online||04 May 2018|
A Mach-sensitive splitting approach for Euler-like systems
EDF lab Saclay,
7 boulevard Gaspard Monge
2 I2M, UMR CNRS 7373 Technople Château-Gombert 39, rue F. Joliot Curie 13453 Marseille Cedex 13, France
3 IMSIA, UMR EDF/CNRS/CEA/ENSTA 9219 Université Paris Saclay 828 Boulevard des Marchaux 91762 Palaiseau Cedex, France
4 DEN/SEMT, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
5 EDF lab Chatou, 6 Quai Watier 78400 Chatou, France
* Corresponding author: email@example.com
Accepted: 18 December 2017
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.
Mathematics Subject Classification: 35L40 / 76N15
Key words: Operator splitting, fractional step / hyperbolic / low mach number flows / relaxation schemes
© EDP Sciences, SMAI 2018
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