Maritime structures in heavy seas can experience wave impact events with high loads. The loads can lead to structural failure and even loss of life. Wave breaking in said sea states causes air to be entrained in water as aeration cloads, remaining long enough to be transported and to play a role in the impulsive interaction with the structure. A small amount of air in water already forms a highly compressible mixture. Compressibility influences the magnitude of the impact loads. A new cartesian grid method for compressible multiphase flow is introduced to account for water, air and homogeneous mixtures of air and water. The method is designed to predict the hydrodynamic loads on moving bodies engaging with interfaces between fluids having large density ratios. An equation for conservation of energy is omitted by enforcing pressure-density relations. The interface between fluids is transported using a geometric Volume-of-Fluid method. The interface between fluids and structure is taken care of by a cut-cell method. An additional fraction field for the amount of air in water in combination with a new formulation for the multiphase speed of sound prevent overprediction of compressibility by artificial air entrainment. New experimental data of 2D wedge impacts with aerated water, made available as open data, are presented to demonstrate the validity of the numerical method. For low aeration levels, the simulation results in terms of the impact loads on the wedge and the frequencies of pressure waves generated upon impact are in good agreement with the experimental data. Increasing the level of aeration reduces the maximum impact load on the wedge. Reflected density waves lead to secondary loads on the wedge. The intensity of the secondary loads, relative to the primary load of impact, increases with the aeration level while the density wave frequency decreases.

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A new bilinear interface reconstruction algorithm (BLIC) is presented to capture highly-curved interfaces more accurately on structured grids without a significant increase in computational costs compared to the standard piecewise linear interface calculation (PLIC) methods. The new reconstruction algorithm uses the initial PLIC segment and improves continuity of the interface using an averaging method. A curvature-weighted method improves the repositioning of the linear segments. A new unsplit donating quadrant advection (DQA) scheme is introduced that is conservative and can create consistency with the momentum flux for two-phase flow models with a staggered MAC arrangement of variables within a grid cell. The consistent discretization of the fluxes prevents spurious interface velocities, negative densities, and instabilities. Standard 2D test cases and benchmarks demonstrate the performance of the BLIC and the DQA scheme, showing high accuracy and low costs compared to other available methods.

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A deeper understanding of physics is required when the complexity of events increases. A complex event consists of many detailed interacting processes. The complete picture asks for an understanding of each of the processes individually. Numerical computing in the maritime industry is becoming more relevant due to the increase in usability and relatively low costs compared to experiments. The numerical results allow for analysis at the required level of detail. The complexity of water-wave impacts on offshore structures necessitates innovative numerical approaches because conventional analytical techniques fall short of representing the non-linearity in these events....@en

The numerical prediction of two-phase flows with an interface is challenging, to a considerable extent because of the high density ratio at the interface. Numerical results become affected by momentum losses, diverging spurious interface velocities, free surface distortion, and even numerical instability. To prevent issues like these, consistent momentum and mass transport with an additional continuity equation were introduced. In this article, we describe how a consistent discretization was incorporated into our own method and extended for fluid-structure interaction (FSI) with moving rigid bodies. The new method was tested against benchmark simulations from literature confirming that consistent transport modeling gives a significant improvement compared to non-consistent modeling for the dynamics of two-phase flows. Newly devised proof of principle FSI simulations with momentum transfer from fluid to body in the presence of a high-density ratio between fluids are introduced that could serve as a benchmark for future studies. The simulations demonstrate that consistent modeling gives an order of magnitude improvement in terms of momentum conservation compared to non-consistent modeling. Simulations with the new method are also compared to FSI experiments from literature. Results obtained with the consistent method are closer to the measurements than results of the non-consistent method. The merit of consistent modeling with and without FSI becomes especially apparent for two-phase flows with a high-density ratio between fluids.

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Surrogate modelling techniques such as Kriging are a popular means for cheaply emulating the response of expensive Computational Fluid Dynamics (CFD) simulations. These surrogate models are often used for exploring a parameterised design space and identifying optimal designs. Multi-fidelity Kriging extends the methodology to incorporate data of variable accuracy and costs to create a more effective surrogate. This work recognises that the grid convergence property of CFD solvers is currently an unused source of information and presents a novel method that, by leveraging the data structure implied by grid convergence, could further improve the performance of the surrogate model and the corresponding optimisation process. Grid convergence states that the simulation solution converges to the true simulation solution as the numerical grid is refined. The proposed method is tested with realistic multi-fidelity data acquired with CFD simulations. The performance of the surrogate model is comparable to an existing method, and likely more robust. More research is needed to explore the full potential of the proposed method. Code has been made available online at https://github.com/robertwenink/MFK-Extrapolation.

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A significant part of all structural damage to conventional ships is caused by complex free-surface events like slamming, breaking waves, and green water. During these events air can be entrapped by water. The focus of this article is on the resulting air pockets affecting the evolution of the hydrodynamic impact pressure that loads the ship's structure. ComFLOW is a computationally efficient method based on the Navier-Stokes equations with a Volume-of-Fluid approach for the free surface, designed to perform multiphase simulations of extreme free surface wave interaction with maritime structures. We have extended ComFLOW with a Continuum Surface Force (CSF) model for surface tension, thereby completing our method for representing gas-water interaction after free surface wave impacts. The implementation was verified with benchmark cases addressing all relevant aspects of the dynamics of entrapped air pockets. The implementation was validated by means of a dam-break experiment, a characteristic model for green water impact events. The method-having been verified and validated-was applied to a dam-break simulation for a different setting in which the impact on a wall leads to an entrapped air pocket. Surface tension was found not to have an influence on entrapped air pocket dynamics of air pockets with a radius larger than 0.08 [m]. For wave impacts it was found that the effect of compression waves in the air pocket dominates the dynamics and leads to pressure oscillations that are of the same order of magnitude as the pressure caused by the initial impact on the base of the wall. The code is available at: https://github.com/martin-eijk/2phase.git.

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