Numerical Modeling of Two-Fluid Interfacial Flows
Numerical Modeling of Two-Fluid Interfacial Flows
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发表时间：
2001
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通讯作者：
A. Smolianski
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作者：
A. Smolianski
Jyväskylä：Jyväskylä大学，2001年，109页(Jyväskylä计算研究ISSN 1456-5390；8)ISBN 951-39-0929-8芬兰摘要Diss。本文对自由运动界面分离的两种不相容粘性流体的非定常流动进行了研究。本工作的目的是在考虑到可能的界面拓扑变化(如合并或解体)和实际的宽范围的物理参数的情况下，为所有类型的双流体界面流动的数值模拟制定一个统一的策略。这种计算方法本质上依赖于三个基本组成部分：用于空间逼近的有限元方法、用于时间离散的算子分裂方法和用于界面表示的Level-Set方法。有限元离散是基于问题的变分形式，因此，允许自然地合并不连续的材料系数和奇异的界面集中力。使用有限元可以精确地定位界面，而不需要引入任何人工参数，如界面厚度。我们还表明，采用梯度平均技术后，可以以二阶精度恢复界面法线和曲率，这使得我们能够准确地计算表面张力。对于时间离散化，我们使用了一种算子分裂，从而分离了问题的所有主要困难。这种方法特别使我们能够实现速度和压力的等阶内插。为了模拟涉及界面拓扑变化的现象，我们使用了Level Set方法，与标准的有限差分Level Set实现相比，它的有限元实现带来了一些额外的好处。我们还介绍了一个简单的质量校正过程，允许保持一个最优的，二阶精确的质量守恒。数值算例包括气泡动力学模拟、分叉喷流模拟和Rayleigh-Taylor不稳定性模拟。
Smolianski, Anton Numerical Modeling of Two-Fluid Interfacial Flows Jyväskylä: University of Jyväskylä, 2001, 109 p. (Jyväskylä Studies in Computing ISSN 1456-5390; 8) ISBN 951-39-0929-8 Finnish summary Diss. The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. The goal of the present work is to elaborate a unified strategy for numerical modeling of all kinds of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The presented computational approach essentially relies on three basic components: finite element method for spatial approximation, operator-splitting for temporal discretization and level-set method for interface representation. Finite element discretization is based on variational formulation of the problem and, thus, allows to naturally incorporate discontinuous material coefficients and singular interface-concentrated forces. The use of finite elements permits to localize the interface precisely, without introduction of any artificial parameters like interface thickness. We also show that interface normal and curvature can be recovered with the second-order accuracy after applying a gradient averaging technique; that allows us to compute accurately the surface tension force. For temporal discretization we employ an operator-splitting, thus, separating all major difficulties of the problem. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. In order to model the phenomena involving interface topology changes we make use of the levelset approach, the finite element implementation of which brings some additional benefits as compared to the standard finite difference level-set realizations. We introduce also a simple mass-correction procedure allowing to maintain an optimal, second order accurate mass conservation. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the proposed computational method.