Simulation of compressible two-phase flows with topology change of fluid-fluid interface by a robust cut-cell method

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• 作者：Jian-Yu Lin ; Yi Shen ; Hang Ding ; ^{hding@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Nan-Sheng Liu ; Xi-Yun Lu
• 关键词：Cut-cell method ; Level-set function ; Sharp-interface method ; Compressible two-phase flows
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：328
• 期：Complete
• 页码：140-159
• 全文大小：4502 K

文摘

We develop a robust cut-cell method for numerical simulation of compressible two-phase flows with topology change of the fluid–fluid interface. In cut cell methods the flows can be solved in the finite volume framework and the jump conditions at the interface are resolved by solving a local Riemann problem. Therefore, cut cell methods can obtain interface evolution with high resolution, and at the same time satisfactorily maintain the conservation of flow quantities. However, it remains a challenge for the cut cell methods to handle interfaces with topology change or very high curvature, where the mesh is not sufficiently fine to resolve the interface. Inappropriate treatment could give rise to either distorted interface advection or unphysical oscillation of flow variables, especially when the regularization process (e.g. reinitialization in the level set methods) is implemented. A robust cut-cell method is proposed here, with the interface being tracked by a level set function. The local unphysical oscillation of flow variables in the presence of topology change is shown to be greatly suppressed by using a delayed reinitialization. The method can achieve second-order accuracy with respect to the interface position in the absence of topology changes of interface, while locally degrading to first-order at the interface region where topology change occurs. Its performance is examined through a variety of numerical tests, such as Rayleigh collapse, shock-bubble interaction, and shock-induced bubble collapse in water. Numerical results are compared against either benchmark solutions or experimental observations, and good agreement has been achieved qualitatively and/or quantitatively. Finally, we apply the method to investigating the collapse process of two tandem bubbles in water.