Flow pattern investigation of bionic fish by immersed boundary–lattice Boltzmann method and dynamic mode decomposition

The investigation of fish swimming is prevalent in the fields of biomimetic hydrodynamics and is important for research on the temporal–spatial evolvement of vortex structures around fish, the design and development of propulsion systems, the shape and structural design of bionic robot fish, and the energy-saving control of schooling robot fish swimming. Conventional numerical simulations of fish swimming depend on mesh establishment and testing. However, the deforming body of a swimming fish largely affects local grids and results in low simulation accuracy due to the uncertainties of mesh resolution and structures. The immersed boundary method adopted in this paper has many advantages, it can efficiently capture the details of the complex dynamics of solid surfaces. Through this method, the fish surface is discretized into Lagrangian points with dynamic coordinates for the performance of complicated dynamic motions. In this work, the immersed boundary–lattice Boltzmann method algorithm with a multi-direct forcing scheme based on Palabos is tested with the cases of flow past a sphere to validate its precision. Then, a function of harmonic oscillation is coupled with fish surface points to perform the level swimming of the RoboTuna fish at different Reynolds numbers. The evolvements of vortex structures around the fish body are analyzed on the basis of the Q-criterion. The processes of the deformation of streamlines around the fish tail into local swirling by tail paddling are revealed, and an angle of approximately 30° between the outer edges of the velocity contour and the line cross of the fish head emerges after the fluid domain develops into a stable state. Then, the data of the fluid fields are subjected to dynamic mode decomposition (DMD), wherein the single mode reveals the presence of up-and-down and axisymmetric patterns behind the fish body. Reconstruction and error calculation are performed to validate the accuracy of the DMD model, then DMD prediction is performed to obtain the flow pattern in the future state and error analysis is conducted. In this work, the mutual effects of the swimming fish and the fluid fields, the formation processes of the vortical fields around the fish tail, and the temporal–spatial evolvements of the structural dynamics of the fluid fields behind the fish body are investigated to provide fundamental information to investigations on propeller systems, flexible propulsion devices, the mechanisms of energy extraction from fluids by the fish tail, and the energy-saving strategies of fish schooling.