Abstract The Rayleigh-Taylor instability (RTI) is the instability at the interface between two fluids when a heavier fluid is placed on top of lighter fluid in a gravitational field. In the present work, the RTI was studied numerically by using a meshless radial basis function (RBF) method. The present manuscript describes the development of the meshless RBF method to solve the RTI problem in an incompressible viscous two-phase immiscible fluid. This method can address the difficulty of the classical base method which often requires much computing time for the generation of the computational mesh. Moreover, the meshless RBF method does not require connectivity information among the nodes. Consequently, the present manuscript provides a new numerical procedure in the solution of the RTI problem by the combination of meshless RBF and Cahn-Hilliard equations. In the present numerical study, the RBF method was combined with the domain decomposition method (DDM) to solve the large scale problem. The problem was governed by the Navier-Stokes and Cahn-Hilliard equations in a primitive variable formulation. The Cahn-Hilliard equations were used to capture the interface between two fluids systems. The RBF method was used for spatial discretization and the Euler implicit method was implemented for time discretization. The fractional step scheme was used to solve the pressure velocity coupling. Here, the effects of Atwood numbers as representing the density ratio on the RTI were investigated. As a result, it was found that the position of the rising bubble and falling spike during RTI conforms well to the results from the previous works.

中文翻译：

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基于径向基函数 (RBF) 方法的无网格数值模型模拟 Rayleigh-Taylor 不稳定性 (RTI)

摘要 Rayleigh-Taylor 不稳定性 (RTI) 是在重力场中较重的流体置于较轻的流体之上时两种流体界面处的不稳定性。在目前的工作中，通过使用无网格径向基函数 (RBF) 方法对 RTI 进行了数值研究。本手稿描述了解决不可压缩粘性两相不混溶流体中的 RTI 问题的无网格 RBF 方法的发展。该方法可以解决经典基础方法的困难，该方法通常需要大量计算时间来生成计算网格。此外，无网格 RBF 方法不需要节点之间的连接信息。最后，本手稿通过结合无网格 RBF 和 Cahn-Hilliard 方程提供了解决 RTI 问题的新数值程序。在目前的数值研究中，RBF 方法与域分解方法（DDM）相结合来解决大规模问题。该问题由原始变量公式中的 Navier-Stokes 和 Cahn-Hilliard 方程控制。Cahn-Hilliard 方程用于捕捉两种流体系统之间的界面。空间离散化采用RBF方法，时间离散采用欧拉隐式方法。分步法用于求解压力速度耦合。在这里，研究了代表密度比的阿特伍德数对 RTI 的影响。因此，