Abstract Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region.

中文翻译：

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使用 NAVIER-STOKES 方程的数值解研究具有界面的瞬态流

摘要 考虑了毛细管力和重力，考虑了两种不可混溶流体的流动。使用二维公式中的粘性不可压缩流体模型来描述流动。Navier-Stokes 方程通过扩展的有限元方法进行数值求解，该方法允许界面上存在强烈的不连续性。使用水平集方法跟踪界面位置。这种方法可以研究具有不同接口拓扑结构的流。计算结果针对上升的 2D 气泡、瑞利-泰勒不稳定性的发展以及在扩展区域中沿垂直壁流下的薄膜问题给出了计算结果。