Upwind Stabilized Finite Element Modelling of Non-hydrostatic Wave Breaking and Run-up

In the following report a new methodology is presented to model the propagation, wave breaking and run-up of waves in coastal zones. We represent the different coastal phenomena through the coupling of non-linear shallow water equations with the extended Boussinesq equations of Madsen and Sørensen. Each of the involved equations has a major role in describing a particular physical behaviour of the wave: the latter equations permit to model the propagation, while the non-linear shallow water ones lead waves to locally converge into discontinuities. We start from the third-order stabilized finite element scheme for the Boussinesq equations, developed in a previous scientific work (Ricchiuto and Filippini, J.Comput.Phys. 2014) and develop a non-linear variant, and detach the dispersive from the shallow water terms. A shock-capturing technique based on local non-linear mass lumping that permits in the shallow water regions to degrade locally the scheme to a first-order one across bores (shocks) and dry fronts is proposed. As for the detection of the breaking fronts, the shallow water areas, this involves physics based breaking criteria. We present different definitions of the breaking criterion, including a local implementation of the convective criterion of (Bjørkavåg and H. Kalisch, Phys.Letters A 2011), and the hybrid models of (Kazolea et. al, J.Comput.Phys. 2014), and (Tonelli and Petti, J.Hydr.Res. 2011). The behavior of different breaking criteria is investigated on several cases for which experimental data are available.On décrit une approche pour la simulation de la propagation et déferlement des vagues en proche cote basée sur la couplage entre les équations de Boussinesq améliorées de Madsen and Sorensen, pour la propagation, et les équations Shallow Water, pour le déferlement et le runup. La contruction de ce modele hybride passe d'abord la proposition une variante non-linéaire du schéma élément finis stabilisé de (Ricchiuto and Filippini, J.Comput.Phys. 2014) capable de résoudre les chocs de maniere monotone. Cela est obtenu par un operateur locale de condensation de la matrice de masse qui réduit le schéma de (Ricchiuto and Filippini, J.Comput.Phys. 2014) au schéma de Roe classique. Le couplage entre le modèle Boussinesq et Shallow Water est en suite étudié. On considere différents critères physiques de détection de fronts déferlants. En particulier, on présente une implémentation numérique locale du critère convectif de (Bjorkavag and H. Kalisch, Phys.Letters A, 2011), qui est comparée au critères proposés dans (Kazolea et. al, J.Comput.Phys., 2014) et (Tonelli and Petti, J.Hydr.Res. 2011). Le modèle obtenu est validé sur des nombreux benchmarks avec données expérimentales

Нелінійна динаміка — 2013

The book of Proceedings includes extended abstracts of presentations on the Fourth International conference on nonlinear dynamics

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Experimental and numerical studies of droplet impact on flowing liquid films

Droplet impact on flowing liquid films constitutes an important research area due to its manifold applications both in industry and day-to-day living. Previous studies have, however, ignored the contributions of stochastic waves to the drop impact dynamics. In this project, an experimental study of droplet impact on controlled flowing liquid films is carried out. The aim of the study is to provide an understanding of the contributions of the spatial structures of waves to drop impact dynamics on flowing films. The experimental facility consists of a falling film rig which comprises film flow, film control, and droplet-generation units, as well as a high-speed imaging system. In a preliminary study, the effect of film control on the dominant wave propagation modes is investigated. Two classes of waves are identified, namely the gamma I and II wave families, which are characterised both qualitatively and quantitatively and confirmed to be in good agreement with previous studies in the literature. Studies on the interaction patterns between doubly-excited planar pulse waves on an uncontrolled flowing film surface are then carried out to provide insight into the interaction patterns of waveforms on flowing liquid films. Distinct interaction modes are found to be of central importance to understanding the complex wave interactions which could lead to interfacial ‘turbulence’. The effect of film control on the impact dynamics of both low and high-inertia drops is then studied. In both studies, the impact surface is divided into the “wave hump”, “flat film”, and “capillary waves” regions. For low-inertia drop impacts, film control is observed to have a qualitative and quantitative effect on the length of liquid columns formed in a partial coalescence outcome, the pinch-off time, as well as the size of the ejected daughter droplets. Qualitative differences included a complete change of the outcome, with other outcomes such as ‘bouncing’, ‘sliding’, and ‘total coalescence’ observed in the low-inertia drop impact scenario. For high-inertia drop impacts, the effect of film control is studied in the morphology of the crown produced in a splash outcome as well as the distinctive attributes of the ejected droplets. Significant quantitative differences are observed in the features of the crown such as its structure, diameter, height, wall thickness, facing-direction, coalescing time, and baseline propagation modes, as well as the number and size distribution of the ejected secondary droplets. Finally, numerical studies of the flow situations investigated experimentally are also carried out using two novel codes, one using interface-capturing and adaptive, unstructured meshes, the other employing a hybrid interface-tracking/level-set technique on structured meshes. The numerical results obtained show very good agreement with the experimental studies both qualitatively and quantitatively.Open Acces