Abstract
To explore the influence of inter-formation variables on swimming performance during fish schooling, this paper adopts the sharp interface immersed boundary method based on virtual cells to conduct numerical research on the swimming of three-fish and four-fish swarms with different formations and spacings. The study finds that both streamwise spacing and lateral spacing have significant impacts on the swimming performance of fish schools. In the three-fish formation, when the tandem arrangement has a streamwise spacing of 1.3 times the body length (L), the trailing fish achieve the highest swimming efficiency; when the parallel arrangement has a lateral spacing of 0.25L, the fish in the middle position exhibits the optimal swimming performance. In the four-fish formation model, fish in symmetric positions within the same swarm have similar hydrodynamic performance. For the diamond formation, under the configuration of streamwise spacing 1.2L and lateral spacing 0.5L, the propulsive efficiency of the trailing fish is markedly diminished; however, for the rectangular formation, all trailing fish obtain lower swimming efficiency, and a stable 2S-type vortex structure appears in the wake under the configuration of streamwise spacing 1.5L and lateral spacing 0.5L, which is conducive to thrust generation. The conclusions of this paper can provide certain hydrodynamic advantages and support the development of bionic underwater vehicles and robot technology.