Parameter Sensitivity for Wave-Breaking Closures in Boussinesq-Type Models

Abstract

We consider the issue of wave-breaking closure for the well known Green-Naghdi model and attempt at providing some more understanding of the sensitivity of some closure approaches to the numerical set-up. More precisely and based on [16] we used two closure strategies for modelling wave-breaking of a solitary wave over a slope. The first one is the hybrid method consisting of suppressing the dispersive terms in a breaking region and the second one is an eddy viscosity approach based on the solution of a turbulent kinetic energy model. The two closures use the same conditions for the triggering of the breaking mechanisms. Both the triggering conditions and the breaking models themselves use case depended / ad/hoc parameters which are affecting the numerical solution wile changing. The scope of this work is to make use of sensitivity indices computed by means of Analysis of Variance (ANOVA) to provide the sensitivity of wave breaking simulation to the variation of parameters such as the mesh size and the breaking parameters specific to each breaking model. The sensitivity analysis is performed using the UQlab framework for Uncertainty Quantification [24].

Full Nonlinearity in Weakly Dispersive Boussinesq Models: Luxury or Necessity

“…The interested reader car refer to e.g. [23] for a study on the sensitivity of breaking closures, or to [29] for a thorough study of this case using the hybrid closure. So far, we do seem to see some sort of trend, suggesting that weakly-nonlinear amplitude-flux models such as the MS and NA provide consistently results close to the fully nonlinear 13 GN model up to the breaking point.…”

A hybrid FV/FD scheme for a novel conservative form of extended Boussinesq equations for waves in porous media

“…The hybrid wave breaking strategy is widely used with BT models due to its easy implementation. The interested reader can find more information on the topic in [37,38]. The treatment can be divided into two parts.…”

Introduction to the Special Issue on Numerical Methods and Applications for Waves in Coastal Environments

“…In the Parameter sensitivity for wave breaking closures in Boussinesq-type models [11], the authors Joshi, Kazolea and Ricchiuto are considering the issue of wave breaking closure for the weakly dispersive fully nonlinear equations of Green-Naghdi. The authors make use of the sensitivity indices computed by means of Analysis of Variance (ANOVA) to provide the sensitivity of wave breaking simulation, using two different wave breaking closures, to the variation of parameters such as the mesh size and the breaking parameters for each breaking model.…”

“…Problems arising from fundamental research and real applications in coastal environments demand accurate descriptions of both breaking inception and the details of the breaking process [1,[12][13][14]16,18]. The directions of research that the works of this issue attempt to contribute are the identification and classification of different type of wave breaking [6], the reduction of the computational cost in the accurate description of wave breaking using non hydrostatic Reynolds Averaged Navier-Stokes equations [10], and the understanding of the wave breaking closures for Boussinesq type models [11].…”