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Numerical Modelling of Coupled Potential and Viscous Flow for Marine Applications

A numerical framework for coupling arbitrary potential flow with fully nonlinear, two–phase and turbulent Computational Fluid Dynamics model is presented in this work, where the primary focus of this thesis is the development of viscous model. The model is implemented in arbitrary polyhedral Finite Volume method in foam–extend, a community driven fork of the open source Open Field Operation And Manipulation software. The present model relies on the Ghost Fluid Method for discretisation of jump conditions, yielding infinitesimally sharp density and pressure jumps across the free surface. Interface capturing is achieved with implicitly redistanced Level Set method derived from the Phase Field equation, yielding good conservation properties and rendering additional redistancing steps unnecessary. The potential and viscous flow coupling is achieved via Spectral Wave Explicit Navier–Stokes Equations approach, where the solution is decomposed into incident potential flow solution and perturbation components, facilitating wave transport. Wave reflection is prevented by using relaxation zones with implicit treatment in the far–field. All methodologies are mathematically or numerically reformulated to adhere to strongly conservative, compact stencil, polyhedral Finite Volume method. The numerical model is validated and verified on four sets of test cases: free surface flow over a ramp, wave propagation, assessment of higher order forces on a vertical cylinder due to wave diffraction and seakeeping of a ship in head and oblique regular waves. The computational results compare well with analytical, other numerical and experimental results. A strong emphasis is given to numerous sensitivity studies addressing numerical uncertainties.

Marine hydrodynamics, Free surface flows, Ghost Fluid Method, Implicitly redis- tanced Level Set method, Solution and domain decomposition, Polyhedral Finite Volume method, OpenFOAM, Validation and verification

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