Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well-defined test cases, in two dimensions, of waves generated by a heaving semi-immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open-source code SPHysics (http://www.sphysics.org)§Update made here after initial online publication. is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11:529–551). For wave loading on a half-submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105:421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL-based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

https://inside.mines.edu/~pamartin/ref-paps/neiljfm.pdf

Scattering of water waves by submerged plates using hypersingular integral equations

Scattering of water waves by submerged curved plates and by surface-piercing flat plates

We consider one-dimensional hypersingular integral equations over finite intervals; the integral must be interpreted as a finite-part integral. Such equations arise naturally in various physical situations, involving thin rigid bodies or cracks; examples are given. A method is developed for determining the behaviour of the solution to a hypersingular integral equation near the end-points of the interval of integration. The method uses the Mellin transform. Several examples are worked out in detail.

End-Point Behaviour of Solutions to Hypersingular Integral Equations

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081003145

Irregular frequencies and the motion of floating bodies

The mean position of the cylinder is in the mean free surface, and the cylinder is oscillating vertically (heaving) with a simple harmonic motion of small amplitude. The problem is studied both theoretically and experimentally. The present paper may be regarded as a sequel to an earlier paper (Ursell, Dean & Yu 1959) on the waves due to a piston wave-maker.

Y. S. Yu

Papers

Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment