Lead Research Organisation: City, University of London
Department Name: Sch of Engineering and Mathematical Sci


Considerable advances have been made in the modelling of wave hydrodynamics and wave-body interaction in recent years. Wave diffraction analysis based on potential flow theory is now standard with linear and second-order theory in the frequency domain. In the time domain for fully nonlinear analysis arguably the most versatile, robust and efficient method is the arbitrary Lagrange-Euler finite-element method (QALE-FEM) approach for potential flow, capable of covering 3-D domains of say 20x20 wavelengths in plan with 20 wave periods on overnight runs on an 8-core processor. However, the method is single-phase with the physical limitation of an irrotational, inviscid fluid. Extreme loads and impacts or slam generally involve breaking wave conditions where multi-phase (air-water-solid) behaviour is significant. An alternative approach is required for violent flows with complex physics local to a structure or body. Progress with volume-of-fluid (VOF) methods has been applied to wave interactions with columns and coastal structures. However, the most significant advances for violent wave-structure have recently been made using the Smoothed Particle Hydrodynamics (SPH) method. SPH has been an area of promising research for some years due to its versatility in dealing with free-surface flows with overturning, splashing and body interaction. Recent problems with numerical convergence, stability and very noisy pressure have been resolved for single-phase flow through EPSRC funded work through an incompressible, divergence-free, formulation (ISPH). Numerical convergence with high pressure accuracy for several impulsive test cases has been demonstrated with generalised shifting algorithms for eliminating instabilities within the particle distributions. Clearly, predicting high pressure accurately is vital for fluid-body interaction. This has been extended to two-phase flow with the incorporation of a compressible air phase with good results in preliminary tests. The main disadvantage of SPH is the computational time due to the large number of particles required in 3-D, O(10 million - 1 billion), the large number of neighbour interactions per particle, and the relatively small time steps needed. Variable particle sizing and efficient neighbour searching do not enable domain dimensions of many wavelengths in 3-D to be run for many wave periods as generally required for extreme wave-body interaction.

Building on previous work, in this project ISPH and QALE-FEM for wave-structure interaction will be developed in parallel and then coupled achieving efficient computation in two ways:
1. Dynamic adaptive particle sizing, satisfying minimum error conditions or resolving some physical characteristic, e.g. density or vorticity. Promising preliminary results have been obtained in 2-D by the proposers.
2. Coupling an inner SPH domain with an outer nonlinear potential flow domain using an efficient solution method such as QALE-FEM. Dynamic adaptive particle sizing should also be used in the SPH domain.


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Description 1) A hybrid method was formed by combining the fully nonlinear potential method QALE-FEM with meshless SPH method based on fully viscous formulation. The hybrid method is more efficient to deal with interaction between breaking waves and structures.

2) Develop novel approach for modelling interface to ensure the continuity of pressure and the true discontinuity of pressure gradient across the interface; and new efficient formulation for solving pressure equations, used for a meshless method.

3) Develop the formulas for estimating error of different wave models and for selecting the suitable wave model if the error is specified.
Exploitation Route The hybrid method developed in this way may be used by other engineers to efficiently simulating the wave-structure interaction for various marine engineering applications.

The novel approach for modelling interface and new efficient formulation for solving pressure equations may be employed by other researchers to develop better meshless methods.

The formulas for estimating error of different wave models and for selecting the suitable wave model may be useful for engineers to analyse nonlinear wave dynamic problems in a phase-resolved way.
Sectors Energy,Environment,Transport