Low-order fictitious domain method with enhanced mass conservation for an interface Stokes problem

Daniele Corti, Guillaume Delay, Miguel A. Fernández, Fabien Vergnet, Marina Vidrascu
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Abstract

One of the main difficulties that has to be faced with fictitious domain approximation of incompressible flows with immersed interfaces is related to the potential lack of mass conservation across the interface. In this paper, we propose and analyze a low order fictitious domain stabilized finite element method which mitigates this issue with the addition of a single velocity constraint. We provide a complete a priori numerical analysis of the method under minimal regularity assumptions. A comprehensive numerical study illustrates the capabilities of the proposed method, including comparisons with alternative fitted and unfitted mesh methods.
针对界面斯托克斯问题的增强质量守恒低阶虚构域法
对具有浸入式界面的不可压缩流进行虚构域近似时,必须面对的主要困难之一与界面上可能缺乏质量守恒有关。在本文中,我们提出并分析了一种低阶虚构域稳定有限元方法,该方法通过添加单一速度约束来缓解这一问题。在最小正则性假设条件下,我们对该方法进行了完整的先验数值分析。全面的数值研究说明了所提方法的能力,包括与其他拟合和非拟合网格方法的比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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