Evaluation of different equations of state for simulating fluid-solid interaction with the material point method

The simulation fidelity of Fluid–Structure Interaction (FSI) is critical for predicting multi-phase (solid-liquid-gas) interactions that involve large deformations and failure evolution. While the Material Point Method (MPM) offers a robust numerical procedure for those problems, the choice of the Equation of State (EOS) for weakly compressible fluids remains a subject of compromise between computational accuracy and efficiency. Although the linear polynomial, Mie–Grüneisen, and Tait equations are well-established, their relative performance within a unified MPM framework has not been systematically evaluated. This study therefore evaluates these three EOS models using benchmark cases, including dam-break flows and water-column collapse against elastic obstacles of varying stiffness. We assess interface evolution, impact dynamics, and numerical robustness with different kinds of EOS. The simulation results demonstrate that while the Mie–Grüneisen EOS captures thermodynamic effects, it incurs the lowest computational efficiency without yielding corresponding accuracy gains for isothermal flows. The Tait EOS is identified as the optimal choice, providing the most accurate free-surface evolution and fluid-structure interaction behavior with moderate efficiency. These findings offer the practical guidance for EOS selection, minimizing computational expense for the required accuracy in large-scale particle-based FSI simulations.