A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

doi:10.1007/s42967-023-00349-8

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (4): 2265-2294.doi: 10.1007/s42967-023-00349-8

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A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Jim Magiera, Christian Rohde

Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

收稿日期:2023-04-26 修回日期:2023-09-03 接受日期:2023-10-29 发布日期:2024-12-20
通讯作者: Christian Rohde,E-mail:christian.rohde@mathematik.uni-stuttgart.de E-mail:christian.rohde@mathematik.uni-stuttgart.de
基金资助:
Open Access funding enabled and organized by Projekt DEAL.When preparing this manuscript,the authors have kept the COPE guidelines on how to deal with potential acts of misconduct.The research leading to these results received funding from Deutsche Forschungsgemeinschaft (DFG,German Research Foundation) through the project SFB–TRR 75 with the project number 84292822,and the DFG under Germany’s Excellence Strategy-EXC 2075 with the project number 390740016.

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

Jim Magiera, Christian Rohde

Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Received:2023-04-26 Revised:2023-09-03 Accepted:2023-10-29 Published:2024-12-20
Contact: Christian Rohde,E-mail:christian.rohde@mathematik.uni-stuttgart.de E-mail:christian.rohde@mathematik.uni-stuttgart.de
Supported by:
B. Dong is partially supported by the National Natural Science Foundation of China (Grant No. 12261070) and the Ningxia Key Research and Development Project of China (Grant No. 2022BSB03048). Z. Li is partially supported by the Simons (Grant No. 633724) and by Fundación Séneca grant 21760/IV/22. J. Ruiz is partially supported by the Spanish national research project PID2019-108336GB-I00 and by Fundación Séneca grant 21728/EE/22. (Este trabajo es resultado de las estancias (21760/IV/22) y (21728/EE/22) financiadas por la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad, Colaboración Internacional e Intercambio de Conocimiento “Jiménez de la Espada”. (Plan de Actuación 2022)).

摘要/Abstract

摘要： Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is-at present-no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469:111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argonmethane mixtures in several space dimensions. To our knowledge, such compressible twophase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

关键词: Phase transition, Hyperbolic balance laws for multi-component fluids, Multiscale modeling, Moving-mesh methods, Deep neural networks

Abstract: Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is-at present-no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469:111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argonmethane mixtures in several space dimensions. To our knowledge, such compressible twophase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Key words: Phase transition, Hyperbolic balance laws for multi-component fluids, Multiscale modeling, Moving-mesh methods, Deep neural networks

Jim Magiera, Christian Rohde. A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate[J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2265-2294.

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A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

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