基于模态分解的斯托克斯流多尺度有限元方法

A Multiscale Finite Element Method for Stokes Flow Based on Eigenmode Decomposition

  • 摘要: 对内含复杂微型障碍物的流体通道采用直接数值模拟(DNS),过高的网格自由度导致计算成本难以承受。本文提出了一种基于特征模态分解的多尺度超单元方法,面向Stokes流动问题的多尺度几何特征,通过构造满足不可压缩约束和最小耗散能原理的特征流动基函数,将微观尺度的复杂流动行为凝聚为宏观超单元的少量自由度。在此基础上,区分离线与在线计算阶段,在离线阶段提取微结构内的特征流动模式,在线阶段通过全场能量泛函的极小化直接求解宏观流场,建立了一种高效的计算框架。数值结果表明,该方法能够以较低的计算成本准确刻画由复杂几何边界引起的非均匀流动特征。

     

    Abstract: Direct numerical simulation (DNS) of flow channels containing complex micro-obstacles involves an excessively large number of mesh degrees of freedom, leading to prohibitively high computational costs. In this paper, a multiscale super-element method based on eigenmode decomposition is proposed for Stokes flow problems with multiscale geometric features. By constructing characteristic flow basis functions that satisfy the incompressibility constraint and the principle of minimum energy dissipation, the complex flow behavior at the microscale is condensed into a small number of degrees of freedom of macroscopic super-elements. On this basis, the offline and online computation stages are separated: in the offline stage, characteristic flow modes within the microstructure are extracted; in the online stage, the macroscopic flow field is directly solved through minimization of the full-field energy functional, thereby establishing an efficient computational framework. Numerical results demonstrate that the proposed method can accurately characterize the non-uniform flow features induced by complex geometric boundaries at substantially reduced computational cost.

     

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