A spectral boundary element algorithm for interfacial dynamics in two-dimensional Stokes flow based on Hermitian interfacial smoothing

A two-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow is presented. The main attraction of this approach is that it exploits all the benefits of the spectral methods with the versatility of the finite element method. In addition, it is not affected by the disadvantage of the spectral methods used in volume discretization to create denser systems. To achieve continuity of the interfacial geometry and its derivatives at the edges of the spectral elements during the droplet deformation, a suitable interfacial smoothing is developed based on Hermitian-like interpolations. An adaptive mesh reconstructing procedure based on relevant lengths of the spectral elements is also described.