Volume 8, Issue 2
A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow

Adv. Appl. Math. Mech., 8 (2016), pp. 187-212.

Published online: 2018-05

[An open-access article; the PDF is free to any online user.]

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• Abstract

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a level set to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the level set function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.

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@Article{AAMM-8-187, author = {Guo , YonghuiLi , Ruo and Yao , Chengbao}, title = {A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {2}, pages = {187--212}, abstract = {

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a level set to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the level set function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m706}, url = {http://global-sci.org/intro/article_detail/aamm/12084.html} }
TY - JOUR T1 - A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow AU - Guo , Yonghui AU - Li , Ruo AU - Yao , Chengbao JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 187 EP - 212 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m706 UR - https://global-sci.org/intro/article_detail/aamm/12084.html KW - AB -

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a level set to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the level set function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.

Yonghui Guo, Ruo Li & Chengbao Yao. (2020). A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow. Advances in Applied Mathematics and Mechanics. 8 (2). 187-212. doi:10.4208/aamm.2014.m706
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