Irregular wave propagation with a 2DH Boussinesq-type model and an unstructured finite volume scheme

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. Project-Teams CardamomResearch Report n°9008 -December 2016 -24 pages Abstract:The application and validation, with respect to the transformation, breaking and run-up of irregular waves, of an unstructured high-resolution finite volume (FV) numerical solver for the 2D extended Boussinesq-type (BT) equations of Nwogu (1993) is presented. The numerical model is based on the combined FV approximate solution of the BT model and that of the nonlinear shallow water equations (NSWE) when wave breaking emerges. The FV numerical scheme satisfies the desired properties of wellbalancing, for flows over complex bathymetries and in presence of wet/dry fronts, and shock-capturing for an intrinsic representation of wave breaking, that is handled as a shock by the NSWE. Several simulations and comparisons with experimental data show that the model is able to simulate wave height variations, mean water level setup, wave run-up, swash zone oscillations and the generation of near-shore currents with satisfactory accuracy.

Numerical and Experimental Investigation of Wave Overtopping of Barriers

“…is not time dependent, by dividing by ∆A * ξ 1 ξ 2 , and by recalling Equations (13) and (15), Equation (10), expressed in the time-dependent coordinate system defined in Equation (11), becomes:…”

“…The experimental tests are carried out by adopting a nonintrusive and continuous-in-space image-analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves. A comparison between numerical and experimental results, for several wave and water-depth conditions, is shown.Water 2020, 12, 451 2 of 17 issue, a number of models were created solving depth-averaged Boussinesq Equations (e.g., [10][11][12]), which incorporate nonlinear and dispersive properties. Boussinesq-type models are able to simulate both wave propagation (thanks to the modeling of the dispersive terms) and wave breaking (thanks to the shock-capturing property); for this reason, in recent years they were widely used for wave overtopping studies [13].…”

“…Water 2020, 12, 451 2 of 17 issue, a number of models were created solving depth-averaged Boussinesq Equations (e.g., [10][11][12]), which incorporate nonlinear and dispersive properties. Boussinesq-type models are able to simulate both wave propagation (thanks to the modeling of the dispersive terms) and wave breaking (thanks to the shock-capturing property); for this reason, in recent years they were widely used for wave overtopping studies [13].…”

Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

“…Regarding water waves, one may find important numerical and analytical studies of Bussinesq approximation [20][21][22][23][24][25][26][27][28][29]. There is also a Boussinesq approximation with dissipative dynamics and possible density variations [30][31][32][33][34][35].…”

Self-similar analysis of a viscous heated Oberbeck–Boussinesq flow system

“…There is a considerable analytical and numerical effort to solve Boussinesq approximations or similar forms both for waves [29][30][31][32][33][34][35][36][37][38] and for dissipative dynamics with possible density variations [39][40][41][42][43]. Experiments for certain parameter values are also realized [44][45][46].…”