An improved 2D+t incompressible smoothed particle hydrodynamics approach for high-speed vessel waves

The wave-generated resistance force is substantial for high-speed vessels. A thorough understanding of the wave pattern as well as its drag effect is important for improving vessel performance and optimal design. Owing to the existence of highly nonlinear waves and large deformations of the free surface, the mesh-free smoothed particle hydrodynamics (SPH) approach would provide a useful solution technique for such a practical problem. Based on the pioneering study on the combination of weakly compressible SPH with the two-dimensional (2D) + t (time) theory, the present paper carries out a further investigation on the complex wave patterns generated by a high-speed vessel, through coupling the 2D + t theory with an improved incompressible SPH (ISPH) solver. For the solid vessel boundary, a new treatment method of calculating the velocity and acceleration of the regenerated particles near the curved hull is proposed. In addition, a high accuracy numerical scheme based on the simplified finite difference interpolation (SFDI) approach is used to solve the pressure Poisson equation in the ISPH framework. The robustness of the proposed 2D + t ISPH model is demonstrated through the benchmark tests of water entry and practical applications to the self-designed laboratory experiment.