The immersed boundary method (IBM) has been widely employed to study bio-inspired underwater propulsion which often involves the high Reynolds number, complex body morphologies and large computational domain. Due to these problems, the immersed boundary (IB) reconstruction can be very costly in a simulation. Based on our previous work, an improved level-set-based immersed boundary method (LS-IBM) has been developed in this paper by introducing the narrow-band technique. Comparing with the previous LS-IBM, the narrowband level-set-based immersed boundary method (NBLS-IBM) is only required to propagate the level set values from the points near the boundaries to all the points in the narrow band. This improvement reduces the computational cost from O((LD/Δx)3) to O(k(LD/Δx)2). By simulating a steady-swimming Jackfish-like body, the consistency and stability of the new reconstruction method in the flow solver have been verified. Applications to a dolphin-like body swimming and a shark-like body swimming are used to demonstrate the efficiency and accuracy of the NBLS-IBM. The time for reconstructions shows that the reconstruction efficiency can increase up to 64.6% by using the NBLS-IBM while keeping the accuracy and robustness of the original LS-IBM. The vortex wake of the shark-like body in steady swimming shows the robustness, fastness and compatibility of the NBLS-IBM to our current flow solver.

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