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.