A three-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow

In the present study we describe a novel three-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow and/or gravity. The main attraction of this approach is that it exploits all the benefits of the spectral methods i.e., exponential convergence and numerical stability 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. Our algorithm also exploits all the benefits of the boundary element techniques, i.e., a reduction of the problem dimensionality and great parallel scalability. 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 a Hermitian-like interpolation. An adaptive mesh reconstructing procedure based on the relevant lengths of the spectral elements is also described. In addition, we consider the inertialess motion of a buoyant droplet left to rise or sediment near a vertical solid wall and compare our numerical results with analytical predictions. In our study we emphasize the need for computational studies for the accurate determination of droplet migration near solid walls. © 2006 American Institute of Physics. DOI: 10.1063/1.2337572