  In this paper we study the two dimensional motion of three linked rigid
bodies moving through a fluid. The bodies change their orientation relative to
each other in a way which mimics the swimming of fish. In contrast to previous
simulations the bodies are connected by an elastic skin. The skin responds to
the movement of the bodies and the pressure of the fluid and alters the flow
around the bodies. In particular it prevents fluid moving between them. The
system of bodies and skin is similar in appearance to a swimming leech or
tadpole depending on the relative size of the bodies. We simulate the system
using SPH, with three types of particles: liquid particles, boundary force
particles determining the surface of the rigid bodies, and skin particles
defining the elastic skin. The latter interact with each other, and with the
boundary force particles to which they are anchored, by linear spring forces.
The boundary force particles and the skin particles interact with the fluid
particles by pair forces which are similar to the forces used in the Immersed
Boundary method. The algorithm is based on a Lagrangian, and the equations of
motion conserve linear momentum exactly and angular momentum very accurately.
We compare the motion of rigid bodies with and without skin keeping the total
mass of the bodies plus skin fixed. When the ellipses are identical, and the
forward gait is used, the bodies swim ~13% faster when they are connected by
skin, and they require less energy. When the ellipses have different sizes,
with the front ellipse largest, they travel ~39% faster and use less energy.
The algorithm is simple and robust and can be applied to bodies of arbitrary
shape and in domains which include free surfaces and stratified fluids.
