A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

Abstract

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

Are breaking waves, bores, surges and jumps the same flow?

“…Extensive developments and break-through progress have been made recently for a large variety of coastal engineering applications (e.g. Tissier, 2012;Bacigaluppi et al, 2014;Brocchini, 2013;Kazolea, 2014). A key feature, the breaking process, is however not explicitly simulated and missing in these models.…”

“…Physical parameters, such as the height and length of the roller, have to be quantified and criteria have to be defined with critical bounded values to estimate where the waves break and stop breaking. Thus models still need calibration and further improvements (Brocchini, 2013). The turbulent flow dynamics in bubble clouds is a very challenging numerical problem.…”

Performansi Implementasi Numerik Metode Pseudo Spectral pada Model Gelombang 1D Boussinesq

“…Filosofi dasar dari penurunan persamaan Boussinesq adalah bagaimana menyederhanakan dinamika fluida dari gelombang yang berasal dari masalah 3 dimensi (3D) menjadi masalah 2D (yang hanya bergantung pada variabel horizontal saja) tanpa menghilangkan fenomena fisis dari gelombang seperti dispersi, nonlinearitas, shoaling, difraksi, refraksi dan sebagainya. Review tentang perkembangan tipe gelombang Boussinesq dapat ditemukan pada Brocchini [5], Madsen and Fuhrman [9]. Isi dari paper ini adalah sebagai berikut.…”

A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

“…Unfortunately, the NLSWEs with hydrostatic pressure distribution are unable to simulate some dispersive features of water waves (e.g., waves with different frequencies travel at different speeds) ( Walters, 2005 ;Wei and Jia, 2013 ;Yamazaki et al, 2008Yamazaki et al, , 2011 or secondary free-surface undulations at wave fronts or tails (undular bores and shocks generated by dam-break flows or tsunamis), which are dispersive in nature ( Soares-Frazao and Zech, 2002 ;Kim and Lynett, 2011 ). tion, as well as the complex wetting/drying procedures ( Brocchini, 2013 ;Wei and Jia, 2013 ).…”