An efficient Monte Carlo method is developed to perform the stochastic analysis of slamming loads on marine structures. The probability distribution of the maximum impact force during slamming is established for a given stationary sea state. The method is demonstrated by using a uniform wedge and Wagner’s flat plate theory. Stochastic effects related to deadrise angle, flow separation from the knuckle, vertical position of the structure, vertical motion and roll motion are investigated. The statistics of other parameters such as the duration of the slamming event and the maximum penetration of the structure into water are also assessed.

Free-surface flows are found wherever two immiscible fluids come into contact, such as at the interface between water and air in the ocean. Simulations of free-surface flows at high Reynolds numbers are important for the design of coastal, bottom-fixed, and floating structures exposed to ocean waves, as well as partially filled pipes and tanks. The large difference in density between water and air poses problems for numerical approximation across the interface, and the highly non-linear behaviour of the free surface, which can break and overturn, makes separating computations into two different fluid domains difficult. As a model for free-surface flows, Ocellaris solves the variable-density incompressible Navier-Stokes equations with discontinuous density fields,

A benchmark study of 10 different numerical methods for ship motion and load assessment is presented. Pitch motions and midship vertical bending moments are compared to model test results for a containership at zero speed in head regular waves. The wave steepness is varied from 2.1% to 10.5%. The model tests show that pitch and the vertical bending moment (VBM) display nonlinear behavior even for low-steepness waves. It is demonstrated that computational fluid dynamics (CFD) methods can reproduce the ship responses with good accuracy, even in very steep waves, involving green water and parts of the ship going in and out of water. Weakly nonlinear potential-theory methods tend to overestimate the pitch motions and the sagging moments as the wave steepness increases. For the vertical bending moment in steep waves, the 3D panel methods did not give significantly better results than those obtained with the nonlinear strip theories.

Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the solution. We investigate the use of slope limiters for the velocity field to overcome this problem in a way that does not compromise on the mass conservation properties. The equations are discretised using the interior penalty discontinuous Galerkin finite element method that is divergence free to machine precision. A slope limiter made specifically for exactly divergence free (solenoidal) fields is presented and used to illustrated the difficulties in obtaining convectively stable fields that are also exactly solenoidal. The lessons learned from this are applied in constructing a simpler method based on the use of an existing scalar slope limiter applied to each velocity component. We show by numerical examples how both presented slope limiting methods are vastly superior to the naive non-limited method. The methods can solve difficult two-phase problems with high density ratios and high Reynolds numbers---typical for marine and offshore water/air simulations---in a way that conserves mass and stops unbounded energy growth caused by the Gibbs phenomenon.