Fish are observed to school in different configurations. However, how and why fish maintain a stable schooling formation still remains unclear. This work presents a numerical study of the dense schooling of two free swimmers by a hybrid method of the multi-agent deep reinforcement learning and the immersed boundary-lattice Boltzmann method. Active control policies are developed by synchronously training the leader to swim at a given speed and orientation and the follower to hold close proximity to the leader. After training, the swimmers could resist the strong hydrodynamic force to remain in stable formations and meantime swim in desired path, only by their tail-beat flapping. The tail movement of the swimmers in the stable formations are irregular and asymmetrical, indicating the swimmers are carefully adjusting their body-kinematics to balance the hydrodynamic force. In addition, a significant decrease in the mean amplitude and the cost of transport is found for the followers, indicating these swimmers could maintain the swimming speed with less efforts. The results also show that the side-by-side formation is hydrodynamically more stable but energetically less efficient than other configurations, while the full-body staggered formation is energetically more efficient as a whole.

This work presents a numerical study of the collective motion of two freely-swimming swimmers by a hybrid method of the deep reinforcement learning method (DRL) and the immersed boundary-lattice Boltzmann method (IB-LBM). An active control policy is developed by training a fish-like swimmer to swim at an average speed of 0.4 $L/T$ and an average orientation angle of 0${}^{\circ }$. After training, the swimmer is able to restore the desired swimming speed and orientation from moderate external perturbation. Then the control policy is adopted by two identical swimmers in the collective swimming. Stable side-by-side, in-line and staggered formations are achieved according to the initial positions. The stable side-by-side swimming area of the follower is concentrated to a small area left or right to the leader with an average distance of 1.35 L. The stable in-line area is concentrated to a small area about 0.25 L behind the leader. A detailed analysis shows that both the active control and passive self-organization play an important role in the emergence of the stable schooling formations, while the active control works for maintaining the speed and orientation in case the swimmers collide or depart from each other and the passive self-organization works for emerging a stable schooling configuration. The result supports the Lighthill conjecture and also highlights the importance of the active control.

This paper numerically investigates the impact of fluid rheology on the behaviors of a spherical capsule through a microchannel constriction. Different flow scenarios are considered: a Newtonian capsule in a viscoelastic matrix, a Newtonian capsule in a Newtonian matrix, and a viscoelastic capsule in a Newtonian matrix. The results demonstrate that the capsule's lengths undergo oscillations during the passage through the constriction, with three stages of evolution. When approaching the constriction, the capsule respectively experiences increase and decrease in its length and height. While within or exiting the constriction, the length of the capsule continuously decreases, and the height generally increases. As the capsule moves away from the constriction, the capsule relaxes to different profiles in different flows. Detailed analysis on the effects of the fluid viscoelasticity on the capsule's lengths in different stages is provided. In addition, the behaviors of a red blood cell passing through a microchannel constriction are also examined. This study sheds light on the complex behaviors of a spherical capsule and red blood cell in microchannel constriction, emphasizing the significant influence of fluid rheology on their deformation and shape changes.

An accurate and robust feedback control system is of great importance for bionic robotic fish to perform complex tasks. This work presents a numerical study of target-directed swimming for a three-link bionic fish with a feedback control system based on deep reinforcement learning (DRL). The simulation is achieved by using a hybrid method of the DRL method and the immersed boundary–lattice Boltzmann method (IB–LBM). This framework makes use of the high computational efficiency of the IB-LBM for the generation of massive motion data needed in the DRL training. The fish is first trained to swim towards a static target from random orientation and distance. The only information available to the fish is its orientation and distance from the target. It learns an accurate and subtle control policy after the training. Then the control policy is applied to a moving target. Even though the fish encounters some situations that never happened in the training, it can choose appropriate actions to follow the target in close proximity and automatically adapt its velocity with the velocity of the target. Those simulations demonstrate the accuracy, robustness of the control method, and its ability to adapt to new situations.

This study numerically investigates the hydrodynamics of two self-propelled undulating foils in an initial anti-phase, side-by-side configuration. The effects of lateral spacing, undulatory amplitude, frequency, and kinematic mismatches by independently varying amplitude or frequency, are systematically examined. When kinematics are identical, the foils maintain a symmetric formation, with forward speed varying non-monotonically with lateral spacing and power consumption always exceeding solitary swimming. A critical spacing exists where speeds match while energy efficiency remains lower. Under frequency differences, four modes emerge, separating (Se), side-by-side (Ss), bouncing side-by-side (Bs), and staggered (Sg), with the kinematically disadvantaged individual gaining speed and efficiency at the advantaged individual’s energetic expense. Under amplitude differences, formations become more stable. The kinematically disadvantaged individual consistently gains speed with increased power consumption, while energy efficiency gains appear only when disparity is sufficiently large. Further analysis shows that reduced-order models for inline formations fail to capture the observed non-monotonic speed variation and critical spacing. Instead, collective performance in side-by-side configurations is governed by the coupling of full-body lateral velocity fields, rather than wake-vortex or leader’s trailing edge-follower’s leading edge interactions. These findings highlight fundamental differences between anti-phase, side-by-side and inline schooling, demonstrating that kinematic heterogeneity reshapes the distribution of hydrodynamic advantages among individuals.