Dynamic boundary conditions (DBC) for solid surfaces are standard in the weakly compressible smoothed particle hydrodynamics (SPH) code DualSPHysics. A stationary solid is simply represented by fixed particles with pressure from the equation of state. Boundaries are easy to set up and computations are relatively stable and efficient, providing robust numerical simulation for complex geometries. However, a small unphysical gap between the fluid and solid boundaries can form, decreasing the accuracy of pressures measured on the boundary. A method is presented where the density of solid particles is obtained from ghost positions within the fluid domain by linear extrapolation. With this approach, the gap between fluid and boundary is reduced and pressures in still water converge to hydrostatic, including the case of a bed with a sharp corner. The violent free-surface cases of a sloshing tank and dam break impact on an obstacle show pressures measured directly on solid surfaces in close agreement with experiments. The complex 3-D flow in a fish pass, with baffles to divert the flow, is simulated showing close agreement with measured water levels with weirs open and gates closed, but less close with gates open and weirs closed. This indicates the method is suitable for rapidly varying free-surface flows, but development for complex turbulent flows is necessary. The code with the modified dynamic boundary condition (mDBC) is available in DualSPHysics to run on CPUs or GPUs.

This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.

A numerical inconsistency has emerged for multi-phase smoothed particle hydrodynamics simulations when using very high resolution, made possible by graphical processing units. In violent flows unphysical voids and phase separation occur ultimately leading to numerical instability. New Fickian-based particle shifting algorithms with a selectively activated free-surface correction are developed for air–water simulations to prevent the creation of unnatural voids and maintain numerical stability through nearly uniform distributions. Using the shifting algorithm without surface correction in the air phase is recommended, with marginal improvements if the shifting algorithm is not applied in water. However, maintaining shifting in water would avoid possible void occurrence. The improvement is demonstrated using a dry-bed dam break and a sloshing tank case. A 3D case involving the impact of the water flow on an obstacle is compared with experimental data. The multi-phase SPH scheme gives closer agreement with experiment than a single-phase simulation.

A moored multi-body line absorber is an attractive option for offshore wave energy conversion. Laboratory studies have been undertaken to determine capture width with multi-mode excitation and heave resonance for the three-float system M4 where the adjacent float spacing is about half a typical wavelength giving anti-phase forcing. The floats increase in diameter and draft from bow to stern and the bow and mid float are rigidly connected by a beam. A hinge with a damper above the mid float absorbs power from the relative rotation between the bow/mid float and the stern float. The resonant heave frequency for each float is different. Anti-phase surge forcing between mid and stern floats is substantial, while there is no hydrostatic stiffness producing resonance. This represents a hydrodynamically complex system and the laboratory experiments indicate high overall capture widths in irregular waves across a range of peak periods without damping optimisation. With different spectral peakedness and directional spread, the capture width is greater than 20 % of a wavelength (based on the energy period) across a range of peak periods typical of an offshore site for floats with a rounded base. The maximum capture width was about 37 % of a wavelength with rounded base floats; having rounded rather than flat bases increased energy capture by up to 60 % by reducing energy losses due to drag. For floats with flat bases comparisons with a geometrically scaled device five times larger and with similar magnitudes of equivalent damping showed similar capture widths as a proportion of wavelength.

Ocean waves provide a promising and abundant renewable energy resource. One reason wave energy technology is still not mature enough for commercialization is the high unit cost of generated electricity. This needs to be improved by combination of device and associated controller design. A multi-float and multi-mode-motion WEC (M-WEC) enables much higher energy conversion compared with a single-float, single-mode WEC (S-WEC); however, the added complexity in dynamics of an M-WEC makes the corresponding controller design more challenging. While all WEC control research has been based on the control of S-WECs it has shown that control can significantly improve energy conversion. This paper aims to design a linear non-causal optimal controller for a M-WEC to demonstrate that this improvement also applies to more complex systems with greater capacity and potentially lower electricity cost. We choose a multi-body attenuator type M-WEC called M4 for which the desirable feature of predominantly linear dynamics has been demonstrated. This means that a linear controller can be designed within a linear hydrodynamic model without introducing an intractable computational burden for real-time controller implementation. Numerical results show that the designed controller can significantly improve the performance of M4 over various wave periods by 40% to 100%.