{"title":"2D conservative sharp interface method for compressible three-phase flows: Ternary fluid flows and interaction of two-phase flows with solid","authors":"Zhu-Jun Li , Yi Ren , Yi Shen , Hang Ding","doi":"10.1016/j.jcp.2025.114187","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we propose a 2D conservative sharp interface method to simulate compressible three-phase flows that encompasses both ternary fluid flows and two-phase flows involving complex solid geometries. The evolution of the fluid-fluid interfaces and the geometry of the solid objects are tracked by a regional level-set function, and are repeatedly reconstructed on a background Cartesian mesh using line segments at each time step. To achieve a high resolution of the interfaces, we identify triple points where the ternary fluids meet or where the interface intersects with solid walls during the reconstruction process. Additionally, by exploiting the symmetry and rotational symmetry of fluid (and solid) positions within a cut cell (i.e., a Cartesian cell containing at least two phases), we reduce the configurations of the cut cells from 96 to 6 basic ones for two-dimensional simulations. Special treatment is also implemented for the cell assembly process in the vicinity of triple points. To ensure a unified approach to boundary conditions, we first identify the specific properties of the reconstructed interfaces, and subsequently enforce appropriate boundary conditions (i.e., jump conditions for interfaces and no-penetration conditions for solid walls) through the solution of a local 1D Riemann problem along the direction normal to the corresponding reconstructed interface. We employ a second-order finite volume method within the arbitrary Lagrange-Eulerian framework to discretize the Euler equations, thereby ensuring that the conservation of mass, momentum, and energy is maintained during the flow computation. The accuracy and robustness of the method are evaluated through numerous numerical experiments, including the compressible triple point problem, the interaction between a shock wave and a multi-medium bubble, high-speed droplet impingement on curved surfaces, and the water entry of a sphere at a uniform speed. The numerical results are validated against benchmark solutions available in the literature. Furthermore, the method is shown to effectively preserve the physical symmetry of ternary fluid flows, primarily due to the geometric resolution of the triple points and second-order accuracy in resolving interfaces.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114187"},"PeriodicalIF":3.8000,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002199912500470X","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we propose a 2D conservative sharp interface method to simulate compressible three-phase flows that encompasses both ternary fluid flows and two-phase flows involving complex solid geometries. The evolution of the fluid-fluid interfaces and the geometry of the solid objects are tracked by a regional level-set function, and are repeatedly reconstructed on a background Cartesian mesh using line segments at each time step. To achieve a high resolution of the interfaces, we identify triple points where the ternary fluids meet or where the interface intersects with solid walls during the reconstruction process. Additionally, by exploiting the symmetry and rotational symmetry of fluid (and solid) positions within a cut cell (i.e., a Cartesian cell containing at least two phases), we reduce the configurations of the cut cells from 96 to 6 basic ones for two-dimensional simulations. Special treatment is also implemented for the cell assembly process in the vicinity of triple points. To ensure a unified approach to boundary conditions, we first identify the specific properties of the reconstructed interfaces, and subsequently enforce appropriate boundary conditions (i.e., jump conditions for interfaces and no-penetration conditions for solid walls) through the solution of a local 1D Riemann problem along the direction normal to the corresponding reconstructed interface. We employ a second-order finite volume method within the arbitrary Lagrange-Eulerian framework to discretize the Euler equations, thereby ensuring that the conservation of mass, momentum, and energy is maintained during the flow computation. The accuracy and robustness of the method are evaluated through numerous numerical experiments, including the compressible triple point problem, the interaction between a shock wave and a multi-medium bubble, high-speed droplet impingement on curved surfaces, and the water entry of a sphere at a uniform speed. The numerical results are validated against benchmark solutions available in the literature. Furthermore, the method is shown to effectively preserve the physical symmetry of ternary fluid flows, primarily due to the geometric resolution of the triple points and second-order accuracy in resolving interfaces.
期刊介绍:
Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries.
The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.