Nonlinear effects on hydrodynamic pressure field caused by ship moving at supercritical speed in shallow water

• We use the shallow-water ship dynamics method to study the SHPF.
• We establish a mathematical model with nonlinear and dispersive effects.
• We use the finite difference method and experiment to study the SHPF.
• The nonlinear effects on SHPF under different conditions are analyzed.
• Our mathematical model and calculation method are effective and feasible.

Based on the shallow-water wave potential flow theory and the assumption of a slender ship, a mathematical model has been established for the pressure field caused by ship moving at supercritical speed in shallow water, with nonlinear and dispersive effects taken into account. The finite difference method is used for the numerical calculation of the ship hydrodynamic pressure field (SHPF), with the central and upwind difference schemes as a combination for the second derivative of the nonlinear term. And the artificial viscous terms are added in the hull and upstream boundary conditions to ensure the stability of solving the nonlinear equation. The comparison between the calculated results and the experimental results shows that both the mathematical model and the calculation method are effective and feasible. The analysis of the nonlinear effects of different-depth water, different depth Froude number and different-width channel on SHPF indicates that the closer to the critical speed the ship in sailing, the narrower the channel becomes, the greater the nonlinear effects on SHPF are.