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Volume 15, Issue 3
A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

Meiyan Fu & Tiao Lu

DOI: 10.4208/nmtma.OA-2021-0162

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 715-743.

Published online: 2022-07

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  • Abstract

We propose a hybrid scheme combing the level set method and the multi-component diffuse interface method to simulate complex multi-phase flows. The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface, the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side. An exact Riemann solver, between the Euler equation and the six-equation model with highly nonlinear Mie-Grüneisen equations of state, is developed to predict the interfacial states and compute the phase interface flux. Several numerical examples, including shock tube problems, cavitation problems, air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

  • Keywords

Multi-phase flow, sharp interface, diffuse interface, level set, six-equation model, exact Riemann solver, Mie-Grüneisen equation of state.

  • AMS Subject Headings

76L05, 76T30, 74H15, 68U20, 47E05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-715, author = {Fu , Meiyan and Lu , Tiao}, title = {A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {3}, pages = {715--743}, abstract = {

We propose a hybrid scheme combing the level set method and the multi-component diffuse interface method to simulate complex multi-phase flows. The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface, the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side. An exact Riemann solver, between the Euler equation and the six-equation model with highly nonlinear Mie-Grüneisen equations of state, is developed to predict the interfacial states and compute the phase interface flux. Several numerical examples, including shock tube problems, cavitation problems, air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0162}, url = {http://global-sci.org/intro/article_detail/nmtma/20813.html} }
TY - JOUR T1 - A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows AU - Fu , Meiyan AU - Lu , Tiao JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 715 EP - 743 PY - 2022 DA - 2022/07 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0162 UR - https://global-sci.org/intro/article_detail/nmtma/20813.html KW - Multi-phase flow, sharp interface, diffuse interface, level set, six-equation model, exact Riemann solver, Mie-Grüneisen equation of state. AB -

We propose a hybrid scheme combing the level set method and the multi-component diffuse interface method to simulate complex multi-phase flows. The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface, the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side. An exact Riemann solver, between the Euler equation and the six-equation model with highly nonlinear Mie-Grüneisen equations of state, is developed to predict the interfacial states and compute the phase interface flux. Several numerical examples, including shock tube problems, cavitation problems, air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

Meiyan Fu & Tiao Lu. (2022). A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows. Numerical Mathematics: Theory, Methods and Applications. 15 (3). 715-743. doi:10.4208/nmtma.OA-2021-0162
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