A time-domain framework for ship motions analysis incorporating a quadtree-based non-linear force model

This paper develops a mathematical model of ship motion based on a hybrid Green's function method, incorporating a quadtree algorithm to accurately account for non-linear Froude-Krylov forces. The model is first validated through a series of tests. Subsequently, a parametric study is conducted by simulating the ship's motion in irregular long-crested waves to analyze its response to various parameters. This research contributes to the field in three key ways: it provides a novel method for seakeeping calculations suitable for marine simulators, offers a reference for expanding the scope of non-linear ship motion studies, and establishes the theoretical foundation for implementing ship dynamics in realistic irregular seas. • Based on the quadtree method, this paper constructs a 3D time-domain ship heave and pitch non-linear mathematical model. • The radiation and diffraction use a linear formulation, and the non-linear Froude-Krylov force uses the quadtree method. • The accuracy of the mathematical model is verified by comparing the test results with the 3D time domain results. • A wave spectrum is used to deal with irregular waves, and the accuracy of the irregular waves is verified. • Different parameters are set to predict the heave and pitch motion of the ship under irregular waves.