Simulation of fluid-structure interaction using the density smoothing B-spline material point method with a contact approach

Fluid-structure interaction (FSI) problems with strong nonlinearity and multidisciplinarity pose challenges for current numerical FSI algorithms. This work proposes a monolithic strategy for solving the equations of motion for both the fluid and structural domains under the unique Lagrangian framework of the B-spline material point method (BSMPM). A node-based density smoothing BSMPM (referred to as ds-BSMPM) is proposed to eliminate pressure instability and oscillation in the simulation of weakly compressible fluids, which is straightforwardly implemented using B-spline basis functions without the need for any sophisticated particle search algorithm. The interaction between the fluid and structure is conducted using the Lagrangian multiplier method on the tensor product grid, whose actual position is determined by the Greville abscissa and is used to detect contact. The proposed method is verified and validated against existing numerical approaches and experimental results, demonstrating the effectiveness of the proposed method in eliminating the oscillations of water pressure and solid stress, and avoiding premature and erroneous contact. In particular, this work presents a promising monolithic approach for achieving high-fidelity solutions to complex FSI problems.