Section: New Results

Modelling of free surface flows

• Participants: Luca Arpaia , Mathieu Colin , Andrea Filippini , Maria Kazolea, Luc Mieussens, and Mario Ricchiuto

• Corresponding member: Mario Ricchiuto

This year we continue our work on fully non-linear weakly dispersive wave models in two dimensional horizontal coordinates. The proposed framework in [92], to approximate the so-called 2D Green-Naghdi equations has been presented in ISOPE (citation) conference an new paper is under preparation.

We also continue our study on wave breaking techniques on BT models [48]. We studied weakly and fully nonlinear models representative of classical and well known models/codes such as BOUSS-2D [85], [86], Funwave [144], [129], Coulwave [109], [131], BOSZ [128], MIKE21 [83], TUCWave [100], [101], and others. We have in particular focused on the enhanced equations of Nwogu [117], and on a frequency enhanced version of the Green-Naghdi system in the form proposed in [69], [93]. We have compared the now popular hybrid closure initially proposed in [136], with an eddy viscosity closure based on an adaptation of the turbulent kinetic energy closure model of [118], modified to be consistent with the detection mechanisms proposed of [101], [93], and also used here. The study performed has involved: a systematic analysis of the behaviour of the two closures for different mesh sizes; the use of dissipation monitors, consistent with the available theory of entropy dissipation for conservation laws [132], [133], to study the dynamics of breaking for several cases; thorough evidence of the equivalent capabilities of the two approaches to provide satisfactory results. Our results indicate that indeed, at least with the (rather standard) implementation proposed here, both closure approaches allow to describe correctly wave transformation and breaking at large scales. We have shown that when using the TKE eddy viscosity closure the numerical dissipation plays a negligible role, which motivates to look for non-dissipative/energy conserving numerical methods in the future. Also, the results clearly show the reduced sensitivity to the mesh of this approach compared to the hybrid one. The analysis of the wave breaking of solitary waves on a slope also has allowed to quantitatively study the interplay of the dissipation introduced by friction, eddy viscosity, and numerical dissipation. A research paper is under review.

Further more we continue our work for weakly non linear weakly dispersive models, on the transformation breaking and run-up of irregular waves. Its is the first time that an unstructured high-resolution FV numerical solver for the 2D extended BT equations of Nwogu is tested on the generation and propagation of irregular waves. A research paper is under review.

The tools developed have been also used intensively in funded research programs. Within the TANDEM project, several benchmarks relevant to tsunami modelling have been performed and several common publications with the project partners are submitted and/or in preparation [6], [140]. We also our code SLOWS, to study the conditions for tidal bore formation in convergent alluvial estuaries [70]. A new set of dimensionless parameters has been introduced to describe the problem, and the code SLOWS has been used to explore the space of these parameters allowing to determine a critical curve allowing to characterize an estuary as "bore forming" or not. Surprising physical behaviours, in terms of dissipation and nonlinearity of the tides, have been highlighted.