Three-dimensional simulation of jellyfish by the penalty immersed boundary method

Abstract

The swimming jellyfish is simulated to investigate the swimming mechanism and efficiency in the framework of the penalty immersed boundary method. For the fluid, the incompressible Navier-stokes equa-tion and the continuity equation are discretized by the fractional step method, while the subdivision FEM is used to solve the solid motion equation. The interaction between the solid and the fluid is realized by the pen-alty immersed boundary method in which the fluid governing equation and the solid governing equation are solved separately by only adding the momentum forcing term. By solving the interaction problem between the fluid and the solid, the swimming mechanism of jellyfish is figured out in present simulation. The representative swimming mechanism of jellyfish consists of the jet propulsion generating thrust by the volume change of the whole bell and paddling propulsion generating thrust by only using the bell margin. The contraction phase is performed by the muscular force, while the relaxation phase is performed by the elastic energy stored in the bell during the contraction. In this simulation, we figure out the effects of elasticity modulus and swimming patterns on the swimming performance. In terms of the elastic property, the propulsive efficiency has the optimal value at the specific tension modulus, since the energy stored during the contraction is dissipated in the low range of the elastic modulus. In terms of the swimming patterns, the propulsive efficiency of the resonant swimming is higher than that of the transient swimming. Additionally, we investigate the effect of the forcing duration, which shows that the propulsive efficiency is proportional to the forcing duration.