Image systems for regularised Stokeslets at walls and free surfaces

Flow around, and hydrodynamic forces on, moving objects can be determined for low Reynolds numbers by superposing elemental Stokeslets to enforce velocity boundary conditions. The method of regularised Stokeslets provides a computationally-practical approach, replacing a sum over singular point elements by one over finite distributed sources. Flow disturbances extend a considerable distance in low-Re flow (typically falling off in magnitude as the reciprocal of distance) and the presence and nature of a nearby boundary cause a profound change to forces on moving objects. Representing boundaries by additional Stokeslets requires significantly more computational resources, so it is common to represent single planar boundaries by the method of images.