Finite cell method for transport problems in porous media
Finite cell method for transport problems in porous media
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发表时间：
2013
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通讯作者：
Q. Cai
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作者：
Q. Cai
这一贡献是将最近提出的用于固体力学问题的有限元方法(FCM)推广到模拟多孔介质中的对流-扩散输运问题。FCM是一种虚拟区域方法和高阶有限元相结合的方法，是一种针对复杂区域的精确计算技术，它不需要生成边界协调网格。高阶有限元方法可以稳定对流占优问题中引入的节点解的振荡。给出了一维和二维模型的指数收敛速度。通过一个三维单组分对流扩散算例和一个基于复杂内部几何结构的二维多组分反应输运问题，研究了该方法在对流和扩散占主导地位的流动中的有效性。
This contribution presents a generalization of the recently proposed Finite Cell Method (FCM) for problems in solid mechanics to the simulation of convection-diffusion transport problems in porous media. The FCM – a combination of a Fictitious Domain approach and high order Finite Elements – is an accurate computational technique for complex domains, which dispenses with the need for generating boundary conforming meshes. The high order FEM will be shown to stabilize the oscillation at nodal solutions introduced in convection-dominated problems. One- and two-dimensional model problems are demonstrated where exponential convergence rates are observed. The validity of the approach is studied for convection- and diffusion-dominated flows, concluding this treatise with a three-dimensional single component convection-diffusion example and a two-dimensional multi-component reactive transport problem based on a complex interior geometrical structure to emphasize the potential of this method.