Stokes Eigenmodes on two-dimensional regular polygons

Abstract

The Stokes eigenmodes on two-dimensional regular polygons of N apexes, 3≤N≤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 λ(N) in the limit of the apex number N→∞, 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.