The Stokes eigenmodes on two-dimensional regular polygons of $N$ apexes, $3\le N\le 40$, are studied numerically using two different solvers: the lattice Boltzmann equation and the Legendre–Galerkin spectral element method. In particular, the lowest 55 eigenmodes on regular $N$-polygons have been computed and investigated for the following properties including (a) symmetries, (b) the asymptotic behaviour of the Stokes eigenvalues $\lambda \left(N\right)$ in the limit of the apex number $N\to \infty$, i.e., in the limit of a regular $N$-polygon becoming its circumcircle, (c) the splitting doublet modes due to boundary geometry of $N$-polygons, and (d) the one-to-one correspondence between the Stokes modes on regular $N$-polygons and on the disc.

二维正多边形上的斯托克斯本征模 $N$ 顶点， $3\le N\le 40$, 使用两种不同的求解器进行数值研究：格子玻尔兹曼方程和勒让德-伽辽金谱元法。特别是，常规上最低的 55 个本征模$N$-polygons 已针对以下属性进行计算和研究，包括 (a) 对称性，(b) 斯托克斯特征值的渐近行为 $\lambda \left(N\right)$ 在顶点数的限度内 $N\to \infty$，即在正则的极限$N$-多边形成为其外接圆，（c）由于边界几何形状的分裂双峰模式 $N$-polygons，以及 (d) Stokes 模式之间的一一对应关系 $N$-多边形和光盘上。