2D+T models for the approximate solution of ship divergent waves are of interest because of the orders of magnitude speed-up that they enable. Nonlinear ship bow waves of slender high-speed vessels are investigated using 2D+T and three-dimensional Cartesian-grid simulations using the conservative Volume-of-Fluid and Boundary Data Immersion Methods to model the fluid and solid interfaces. The formulation of the unsteady two-dimensional problem in this framework is detailed and the results are shown to be quantitatively accurate only when the ship is sufficiently slender and moving at high-speed. The class of bow wave; i.e. non-breaking, spilling, or plunging: is correctly predicted by 2D+T but the location of breaking is not. These deficiencies are overcome to some extent using a Physics-Based Learning Model, which supplements the high-speed 2D+T predictions with a limited set of three-dimensional examples to produce accurate quantitative predictions.
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