Abstract
This paper deals with the numerical approximation of two immiscible incompressible fluids flow. The two-dimensional problem is mathematically described with the aid of the incompressible Navier-Stokes equations. The motion of the two phases is treated with the aid of level set method. The surface tension effects are taken into account as well as the contact angle influence. The problem is formulated in a weak sense and discretized with the aid of the finite element method. The details of the numerical methods are given and several possibilities of the realization of the surface tension term are discussed. Numerical results are shown.
Highlights
The numerical approximation of two-phase flows with free surface is very important in various scientific as well as in technical applications or industrial processes, see e.g. [1], [2], [3]
The approximation of free surface flow influenced by the high surface tension and possibly contact angles is very difficult problem, see e.g. [4], [5], [6], [7], [8]
In order to approximate free surface flows there are several fast, robust and accurate numerical methods available dealing with fixed computing grids
Summary
The numerical approximation of two-phase flows with free surface is very important in various scientific as well as in technical applications or industrial processes, see e.g. [1], [2], [3]. The numerical approximation of two-phase flows with free surface is very important in various scientific as well as in technical applications or industrial processes, see e.g. In order to approximate free surface flows there are several fast, robust and accurate numerical methods available dealing with fixed computing grids. These methods are the marker and cell method [9], volume of fluid method [10] and level set method [11], [12], [13]. The motion of the interface between these two fluids (free surface) is realized using the level set method, cf [11]. The implemented method is verified by solution of a benchmark problem, cf. [4]
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