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In the standard smoothed particle hydrodynamics (SPH) method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Then, concepts of support and dual-support are defined to deal with the unbalanced interactions between the particles with different support domains. Several benchmark problems in one, two and three dimensions are tested to verify the accuracy of the modified SPH model and highlight its advantages over the standard SPH method through comparisons.

Following the approach proposed by Nadaoka et al. [Nadaoka, K., Beji, S. and Nakagawa, Y. (1997) A fully dispersive weakly nonlinear model for water waves, Proc. Roy. Soc. LondonA453, pp. 303–318], we present a set of one-dimensional weakly nonlinear single-component wave equations for rapidly varying topography by including the bottom curvature and squared bottom slope terms ignored in the original equations of Nadaoka et al. To solve the linear version of the extended wave equations derived in this study, a finite difference numerical model is constructed. The performance of the model is tested for the case of wave reflection from a plane slope and a rippled bed. Numerical results are compared with those calculated using other numerical models reported earlier. It is shown that the accuracy of the present numerical model is improved significantly in comparison with that of the original equations of Nadaoka et al. by including a complete set of higher order bottom effect terms for a rapidly varying topography.

This contribution presents a new Artificial Neural Network (ANN) tool that is able to predict the main parameters describing the wave-structure interaction processes: the mean wave overtopping discharge ($q$), the wave transmission and wave reflection coefficients ($K_t$ and $K_r$). This ANN tool is trained on an extended database (based on the CLASH database) of physical model tests, including at least one of the three output parameters, for a total number of nearly 18,000 tests. The selected 15 nondimensional ANN input parameters represent the most significant effects of the structure type (geometry, amour size and roughness) and of the wave attack (wave steepness, breaking, shoaling, wave obliquity). The model can be used for design purposes, leading to a greater accuracy than existing formulae and similar tools for complex geometries for the prediction of $K_r$ and $K_t$, and it has a similar accuracy as the CLASH ANN for predicting $q$.

The assumption of quasi-static electric field in the problem of wave reflection in piezoelectric half-plane results in missing an independent electric wave mode at the piezoelectric boundary, which leads to oversimplified solutions of reflected waves in a strong piezoelectric medium if only elastic bulk wave boundary conditions are considered. The paper presents a novel solution to address the issue by using the inhomogeneous wave theory and introducing a virtual reflection wave mode in addition to the elastic bulk wave modes. The virtual wave is assumed to satisfy the Snell's law as well as the piezoelectric boundary condition and can be treated in the same way as the elastic bulk waves. The analysis results show that this virtual wave always propagates along the boundary for any incident angle and can be treated as a pseudo surface wave. The energy transmission analysis reveals that this surface wave transmits zero energy and does not violate the energy conservation between the incident and the reflected elastic bulk waves. In addition, the analysis also reveals an interesting result that the quasi-transverse, not the quasi-longitudinal, incident wave will be fully reflected and no quasi-longitudinal reflected wave will be generated if the incident angle is beyond a critical angle.