{"title":"轴对称雷利-泰勒不稳定性问题的相场计算无网格模拟","authors":"","doi":"10.1016/j.enganabound.2024.105953","DOIUrl":null,"url":null,"abstract":"<div><p>A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. 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The simulations did not need any upwinding in the range of the simulations. 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引用次数: 0
摘要
基于相场法(PFM)方法,对具有不同密度并受重力影响的不相溶牛顿双液体系进行了表述。相关的纳维-斯托克斯(NS)和卡恩-希勒德(CH)耦合方程的求解采用无网格漫反射近似法(DAM)和压力隐含分算子法(PISO)。所有项都涉及可变密度。相关的移动边界问题是通过笛卡尔和轴对称坐标的单域、不规则、固定节点布置来处理的。无网格 DAM 采用重叠子域上的加权最小二乘法近似、二阶多项式形状函数和高斯权重。与之前用于相关问题无网格求解的 Chorin 压力-速度耦合相比,该求解程序具有更高的稳定性。对阿特伍德数为 0.76 的雷利-泰勒不稳定性问题进行了模拟。DAM 参数(高斯权重函数的形状参数和局部子域中的节点数)与作者以前对单相流的研究相同。模拟范围内不需要任何上卷。结果与使用开源代码 Gerris、开源场操作和操纵(OpenFOAM®)代码进行的基于网格的有限体积法研究以及之前已有的结果进行了很好的比较。
Phase-field formulated meshless simulation of axisymmetric Rayleigh-Taylor instability problem
A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris, Open-source Field Operation and Manipulation (OpenFOAM®) code and previously existing results.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.