The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite difference method (GFDM) together with the second-order Runge–Kutta method (RKM2) is employed to construct a fully three-dimensional (3D) meshless numerical wave flume (NWF). Three numerical examples, i.e., the propagation of freak waves, irregular waves and focused waves, are implemented to verify the accuracy and stability of the developed 3D GFDM model. The results show that the present numerical model possesses good performance in the simulation of nonlinear water waves and suggest that the 3D “RKM2-GFDM” meshless scheme can be adopted to further simulate more complex nonlinear problems regarding wave–structure interactions in ocean engineering.

This paper theoretically and experimentally investigates the inertial effects of the flap body on the performance of a bottom-hinged oscillating wave surge converter (BH-OWSC). A two-dimensional (2D) hydrodynamic theory for a BH-OWSC based on the assumption of potential flow is developed to show that one simple but critical parameter, i.e., the square of sum of three mechanical-impedance terms associated with the inertial effects, can precisely characterize the performance trend of a BH-OWSC. Model testing in a small-scaled wave basin follows to validate the theoretical formulations with a flap body consisting of multiple hollow cylinders into which water can be filled individually to alter the values of flap's inertial parameters. The performance of each inertial specification of the flap model is evaluated based on the measurement of the mean water discharge from the hydraulic pump (or the power take-off). Finally, the “near resonant condition” has been validated experimentally by altering the inertial parameters of the flap. Thus, the aforementioned parameter is shown to be capable of characterizing the inertial effects on the performance of a BH-OWSC, and the minimization of it will maximize the power capturing performance of a BH-OWSC. Consequently, the parameter can be used for design guidelines of the flap body in its inertial aspect, such as locating the center of mass and determining the geometric dimensions of a flap body.

A fictitious domain extension approach is introduced to solve the heat transfer problem in arbitrary domains by the radial basis function collocation method. The concept is derived from the superposition principle of potential problems. In this approach, arbitrary physical geometries which are usually not convex and/or topo‐logical rectangular are extended to domains which are topologically rectangular. The solution domain is also extended to the fictitious area and assumed to satisfy the same governing equation in it and on its boundaries. The boundary conditions are still specified on the boundaries of the original physical domain. The problem in the extended domain becomes ill‐posed. However, it can be easily circumvented by the collocation method. Applying this approach to several test problems with complicated geometries, we demonstrate that the solution can be directly obtained without domain decompositions and iterations. The new approach is simple, efficient and accurate.

A new boundary element procedure which employs dipole‐only singularities is developed to predict the flow past a two‐dimensional cavitating hydrofoil. In the present approach, the unknowns in the discretized simultaneous equation system consist of the dipole strengths at the control points on the wet surface of hydrofoil, the adjusted cavity increments at the nodal points on the cavity surface and the constant tangential speed on the cavity surface. As usual, the nonlinear iteration procedure is adopted; that is, the dynamic and kinematic boundary conditions of the cavity surface are specified on the correct cavity boundary which is a part of the flow solution and unknown before the problem is solved. Some numerical experiments have been carefully conducted. The results show that the present simpler approach successfully predicts the flow, compared to the methods in the literature.