A hybrid numerical model for the collective motion of fish groups

We propose a hybrid numerical model for the collective motion of fish groups, which integrates an agent-based model with a computational fluid dynamics (CFD)-based model. In the agent-based model, the fish group is represented by self-propelled particles (SPPs), incorporating social forces with local interactive rules. The CFD-based model treats the fish body with an undulated filament that responds to the hydrodynamic forces imposed by the surrounding fluid flow. These two models are coupled using a central pattern generator controller. We test this hybrid model with groups of 30–50 individuals. The results show that the group exhibits various collective behaviours, including tight schooling, sparse schooling and milling patterns, by adjusting the coefficients in the SPP model. Due to the hydrodynamic interactions, particularly with the obstacle avoidance model, both the individuals’ and the group’s mean speed fluctuate, differentiating it from traditional SPP models that typically consider volumeless particles. More interestingly, our findings indicate that fish benefit from collective motion in terms of energetic consumption in both schooling and milling patterns. It is important to note that the swimming fish are actuated using a very simple mechanism without any optimisation strategy. An additional study investigates the effects of the Reynolds number, demonstrating the capability of the current hybrid model to account for fish groups of varying body lengths or swimming speeds. Future applications of this model are promising, offering potential insights into the energetic advantages of collective motion in large-scale fish groups.