An implicit moving-least-squares immersed boundary method for high-fidelity fluid-structure interaction simulations

In this work, an implicit moving-least-squares immersed boundary method (MLS-IBM) is proposed to accurately enforce the velocity boundary condition on immersed objects. This method effectively eliminates errors induced by the inequality between the interpolation and spreading operations, while preserving the conservation of the force and torque. The instantaneous discretization errors for the velocity boundary conditions are negligible, approaching machine round-off levels, which renders the proposed method much more accurate than previous MLS-IBMs. In terms of computational efficiency, the proposed implicit MLS-IBM outperforms the explicit variant MLS-IBM for stationary problems and shows comparable performance for moving-boundary problems. Additionally, the assembly of the correlation matrix in the implicit MLS-IBM is optimized to improve the computational efficiency, making it superior to previous implicit IBMs. The proposed implicit MLS-IBM integrated with the lattice Boltzmann flux solver can achieve second-order spatial accuracy through a mesh-refinement study. The robustness and accuracy of the proposed implicit MLS-IBM are validated through several complex fluid-structure interaction (FSI) problems involving complex geometries, moving boundaries, and large deformations.