Numerical simulation of wave phenomena using FreeFEM

In this research free surface motion governed by the shallow water equations is considered. A numerical scheme based on the finite element method, which is incorporated in the open source FreeFEM, was used to simulate several wave phenomena. By carefully setting the corresponding initial condition as well as boundary conditions, several numerical computations were conducted. Numerical simulations presented here are standing wave in a closed basin, progressive wave over a flat bottom, as well as wave shoaling over a decreasing depth and wave refraction. In all cases above, the existing analytical formula are used to validate the numerical results. These computations suggest that explicit-implicit scheme is appropriate for varying water wave simulations.

NUMERICAL INVESTIGATIONS OF THE MECHANISMS ASSOCIATED WITH THE ONSHORE RIPPLE MIGRATION

Quantification of cross-shore sediment transport is one of most intriguing challenges in shoreline and coastal geomorphology. During the past decades, several key mechanisms associated with onshore/offshore sediment transport have been identified, such as wave skewness/asymmetry, progressive wave streaming and undertow current. However, applying these mechanisms to the migration of wave formed bedforms (ripples) is not straightforward. For example, recent field observations off Fire Island, NY showed that ripples migrated onshore even during periods of offshore directed wave skewness, which is contradictory to the prediction of empirical sediment transport formulations. The physical processes driving ripple vortex formation, ejection and boundary layer streaming associated with rippled bed can further complicate the bedload/suspended load sediment transport over ripples. To fully understand these mechanisms, a comprehensive model that can resolve the ripple dynamics and interactions between free surface wave and rippled bed is examined.

A Thévenin-Inspired Approach to Multiple Scattering in Acoustics

We have previously shown how Thévenin's theorem may be used to solve problems in linear acoustic scattering from a mobile body, by forming the solution as a superposition of the field scattered from the body when held immobile and the solution for radiation from the body in a quiescent field (Williams, R. P. and Hall, N. A., 2016, “Thévenin Acoustics” J. Acoust. Soc. Am., 140(6), pp. 4449–4455). For problems involving scattering from multiple mobile bodies, the approach can be extended by using multiport network formalism. The use of network formalism allows for the effects of multiple scattering to be treated using analogous circuit models, facilitating the integration of scattering effects into circuit-based models of acoustic transducers. In this paper, we first review Thévenin's theorem for electrical and linear acoustic systems, and discuss the Thévenin-inspired approach to scattering from one rigid, mobile cylinder. Two-port formalism is introduced as a way to address problems involving two scatterers. The method is illustrated using the problem of scattering from a pair of rigid, mobile cylinders in an ideal plane progressive wave. The velocities of the cylinders and the resultant pressure field in response to the incoming wave are found. Unique features of the method compared to more conventional approaches are discussed.