An efficient boundary element formulation for doubly-periodic two-dimensional Stokes flow with pressure boundary conditions

We present an efficient formulation of the boundary element method (BEM) for calculation of two-dimensional pressure-driven Stokes flow in a doubly-periodic domain. In contrast to similar methods which require a priori knowledge of the mean fluid velocity, this formulation is based on knowledge of the mean pressure gradient only. We present a method of calculating the permeability tensor without the need to specify either mean velocity or pressure gradient. We discuss optimality of the splitting parameter in the doubly-periodic Green's function, with regard to the numerical overhead required for the BEM, and in most cases find a 3-10 fold increase in computational efficiency compared to the splitting parameter used in standard BEM formulations.