In natural environments, fish almost always swim in groups. Investigating the coupled mechanism of biomimetic fish exhibiting autonomous swimming capabilities advances our understanding of fish schooling phenomena and simultaneously aids in refining the structural and formation configurations of underwater robotic vehicles. This work innovatively develops an algorithm based on the Direct-Forcing Immersed Boundary Method (DF-IBM) and implements it in an efficient, modular software program written in C++. The program accelerates the calculation process by using a multigrid method. Validation against a benchmark case of flow around a cylinder, with comparison to data from the existing literature, verifies the program’s precision with discrepancies of less than 3.6%. Based on this algorithm, the paper analyzes the incompressible viscous flow during the movement of parallel-aligned biomimetic fish. It uncovers the interaction between the fish’s motion and the surrounding flow field and also reveals the hydrodynamic mechanisms of the group motion of the parallel-aligned biomimetic fish. The flow field under varying spacing and phases between the parallel-aligned biomimetic fish proves that the interaction between the flow fields induced by the two fish bodies becomes increasingly significant when decreasing the lateral spacing from $1.4L$ to $0.6L$. Notably, an initial lateral convergence of the fish bodies is observed, followed by a sideways swimming pattern at a particular pitch angle, accompanied by a decrement in their forward swimming velocity as they approach each other. Additionally, this study compares flow field alterations in parallel-aligned biomimetic fish with identical lateral spacing but opposing flapping phases. The findings indicate that, irrespective of the phase, the fish exhibit an initial convergence followed by a sideways motion at a specific pitch angle. However, due to disparities in the tail’s flow field, a larger pitch angle is generated when the fish swim in unison. All the findings above will provide a solid theoretical foundation for the design and optimization of underwater robotic vehicles.

This work develops an Updated Lagrangian Smoothed Particle Hydrodynamics (ULSPH) framework to simulate high-speed icebreaking by a hemispherically capped cylinder (HCC). Using a self-programmed C++ code with Drucker–Prager damage criteria, this work systematically analyzes how impact velocity (100–200 m/s), ice thickness (10–40 cm), and impact angle (60–90°) govern structural loads and ice failure modes. The head of the HCC is always the stress concentration area, and the peak value of the impact force increases non-linearly with increasing the initial velocity from 100 m/s to 200 m/s. The increase in ice layer thickness from 10 cm to 40 cm raises the peak value of the impact force by 18.1%. The ice layer deformation shows three-stage characteristics: collision depression, penetration perforation, and through-spray. When the impact angle α is non-vertical, the strain of the ice layer is asymmetrically distributed, and the component of the peak impact force along the y direction increases significantly with the decrease in the impact angle, reaching 129.3 kN at α = 60°. Results reveal velocity-driven nonlinear force amplification, asymmetric strain distribution at oblique angles, and critical stress concentration at the HCC head, providing design insights for polar equipment.