A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

doi:10.1007/s42967-021-00137-2

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (2): 722-750.doi: 10.1007/s42967-021-00137-2

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A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Jonas Zeifang^1,2, Andrea Beck^2,3

1 Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium;
2 Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany;
3 Laboratory of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

收稿日期:2020-09-22 修回日期:2021-04-06 出版日期:2023-06-20 发布日期:2023-05-26
通讯作者: Jonas Zeifang, jonas.zeifang@uhasselt.be;Andrea Beck, andrea.beck@ovgu.de E-mail:jonas.zeifang@uhasselt.be;andrea.beck@ovgu.de
基金资助:
This paper contains some revised and extended results from the first author's PhD thesis work[71]. The authors kindly acknowledge the financial support provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the project GRK 2160/1 "Droplet Interaction Technologies" and through the project no. 457811052. The simulations were performed on the national supercomputer HPE Hawk at the High Performance Computing Center Stuttgart (HLRS) under the hpcdg project.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Jonas Zeifang^1,2, Andrea Beck^2,3

1 Faculty of Sciences, Hasselt University, Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium;
2 Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany;
3 Laboratory of Fluid Dynamics and Technical Flows, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Received:2020-09-22 Revised:2021-04-06 Online:2023-06-20 Published:2023-05-26
Contact: Jonas Zeifang, jonas.zeifang@uhasselt.be;Andrea Beck, andrea.beck@ovgu.de E-mail:jonas.zeifang@uhasselt.be;andrea.beck@ovgu.de
Supported by:
This paper contains some revised and extended results from the first author's PhD thesis work[71]. The authors kindly acknowledge the financial support provided by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the project GRK 2160/1 "Droplet Interaction Technologies" and through the project no. 457811052. The simulations were performed on the national supercomputer HPE Hawk at the High Performance Computing Center Stuttgart (HLRS) under the hpcdg project.

摘要/Abstract

摘要： Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a specific level set ghost fluid method and an implicit-explicit (IMEX) flux splitting is proposed to overcome this timestep restriction. A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface. In this part of the domain, the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases. It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method. Applications to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

关键词: IMEX flux splitting, Level set method, Ghost fluid method, Low Mach number flows

Abstract: Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a specific level set ghost fluid method and an implicit-explicit (IMEX) flux splitting is proposed to overcome this timestep restriction. A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface. In this part of the domain, the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases. It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method. Applications to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

Key words: IMEX flux splitting, Level set method, Ghost fluid method, Low Mach number flows

中图分类号:

Jonas Zeifang, Andrea Beck. A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method[J]. Communications on Applied Mathematics and Computation, 2023, 5(2): 722-750.

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A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

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