A Mach-sensitive implicit-explicit scheme adapted to compressible multi-scale flows

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:340

Article

Iampietro, D.^1,2,5  Daude, F.^1,2  Galon, P.^2,3  Herard, J-M^4,5 

[1] EDF R&D, Dept ERMES, 7 Blvd Gaspard Monge, F-91120 Palaiseau, France

[2] Univ Paris Saclay, IMSIA, UMR EDF CNRS CEA ENSTA 9219, 828 Blvd Marechaux, F-91762 Palaiseau, France

[3] CEA, DEN, DANS, DM2S,SEMT,DYN, F-91191 Gif Sur Yvette, France

[4] EDF R&D, Dept MFEE, 6 Quai Warier, F-78401 Chatou, France

[5] I2M, UMR CNRS 7373, Technopole Chateau Gombert,39 Rue Joliot Curie, F-13453 Marseille, France

关键词: Fractional step;    Implicit-explicit schemes;    Multi-scale flows;    Low Mach number;    Relaxation schemes;    Hyperbolic equations;   

DOI  :  10.1016/j.cam.2018.02.019

来源: Elsevier

【 摘 要 】

The method presented below focuses on the numerical approximation of the Euler compressible system. It pursues a two-fold objective: being able to accurately follow slow material waves as well as strong shock waves in the context of low Mach number flows. The resulting implicit explicit (IMEX) fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow Mach number. When the latter rises suddenly, the IMEX scheme, so far driven by a material-wave Courant number, turn into a time-explicit approximate Riemann solver constrained by an acoustic-wave Courant number. It is also possible to enrich the dynamic splitting in order to capture high pressure jumps even when the flow Mach number is low. One-dimensional low Mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an IMEX Lagrange-Projection method. Besides, numerical results suggest that the stability of the present method holds for any Mach number if the Courant number related to the convective subsystem arising from the splitting is of order unity. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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