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首页> 外文期刊>International Journal for Numerical Methods in Fluids >A simple finite element method for Stokes flows with surface tension using unfitted meshes
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A simple finite element method for Stokes flows with surface tension using unfitted meshes

机译：使用未拟合网格的带表面张力的斯托克斯流的简单有限元方法

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摘要

This paper presents a simple finite element method for Stokes flows with surface tension. The method uses an unfitted mesh that is independent of the interface. Due to the surface force, the pressure has a jump across the interface. Based on the properties of the level set function that implicitly represents the interface, the jump of the pressure is removed, and a new problem without discontinuities is formulated. Then, classical stable finite element methods are applied to solve the new problem. Some techniques are used to show that the method is equivalent to an easy-to-implement method that can be regarded as a traditional method with a modified pressure space. However, the matrix of the resulting linear system of equations is the same as that of the traditional method. Optimal error estimates are derived for the proposed method. Finally, some numerical tests are presented to confirm the theoretical results. Copyright (c) 2015 John Wiley & Sons, Ltd.
机译：本文提出了一种具有表面张力的斯托克斯流的简单有限元方法。该方法使用独立于界面的未拟合网格。由于表面力的作用，压力在界面上会发生跳跃。基于隐式表示界面的水平集函数的属性，消除了压力的跳跃，并提出了一个没有间断的新问题。然后，采用经典的稳定有限元方法来解决新问题。一些技术被用来表明该方法等效于易于实现的方法，该方法可以被视为具有改变的压力空间的传统方法。但是，所得线性方程组的矩阵与传统方法的矩阵相同。针对该方法得出了最佳误差估计。最后，进行了一些数值测试，以验证理论结果。版权所有（c）2015 John Wiley＆Sons，Ltd.

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