Numerical analysis of geometric parameter effects on fish schooling hydrodynamics for bio-inspired applications

• A 3D MDF-IB-RLBM framework is proposed for multi-body fish hydrodynamics with second-order accuracy. • Lateral and longitudinal spacing play distinct roles in governing the intensity of hydrodynamic interactions. • Following fish achieve up to 22% peak thrust gain, which is highly sensitive to geometric spacing. • A staggered six-fish formation creates a stable low-velocity channel via a collective shielding effect. • The central channel provides energy-saving potential, reducing flow velocity by approximately 30%. Through the hydrodynamic analysis of fish schooling, important insights can be provided for the design of bionic underwater vehicles. Aiming at investigating the effects of geometric parameters on thrust and drag, this paper proposes a multi-direct forcing immersed boundary-regularized lattice Boltzmann method (MDF-IB-RLBM). This method achieves second-order spatial accuracy through a multi-iteration correction strategy. The regularized collision operator ensures numerical stability for high-Reynolds-number flows. Additionally, the computational complexity of this method increases only linearly with the number of fish bodies. A RoboTuna model is adopted for numerical experiments. The results show that when the lateral spacing between fish bodies increases from 0.3 to 0.375 body lengths, the peak drag increase of the trunk of the leading fish relative to a single fish decreases from approximately 17% to approximately 9.5%. The peak thrust gain of the trunk of the following fish relative to a single fish reduces from approximately 22% to approximately 15%. Simulations of the V-formation reveal the vortex ring compression effect and low-velocity channel characteristics in the central region. The shielding effect of the leading fish reduces the central flow velocity by approximately 30%.