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Maria Kazolea

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Papers by Maria Kazolea

Low dispersion finite volume/element discretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes

Ocean Modelling, Apr 1, 2023

We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to sol... more We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to solve a fully-nonlinear and weakly-dispersive depth averaged wave propagation model. The FV method is used to solve the underlying hyperbolic shallow water system, while a standard P 1 finite element method is used to solve the elliptic system associated to the dispersive correction. We study the impact of several numerical aspects: the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the well-posedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H 1. We show, based on both heuristic and strong numerical evidence, that numerical dissipation plays a major role in stabilizing the coupled method, and not only providing convergent results, but also providing the expected convergence rates. Finally, the full mode, coupling a wave breaking closure previously developed by the authors, is thoroughly tested on standard benchmarks using unstructured grids with sizes comparable or coarser than those usually proposed in literature.

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

Ocean Engineering

This paper introduces a conservative form of the extended Boussinesq equations for waves in porou... more This paper introduces a conservative form of the extended Boussinesq equations for waves in porous media. This model can be used in both porous and non-porous media since it does not requires any boundary condition at the interface between the porous and non-porous media. A hybrid Finite Volume/Finite Difference (FV/FD) scheme technique is used to solve the conservative form of the extended Boussinesq equations for waves in porous media. For the hyperbolic part of the governing equations, the FV formulation is applied with Riemann solver of Roe approximation. Whereas, the dispersive and porosity terms are discretized by using FD. The model is validated with experimental data for solitary waves interacting with porous structures and a porous dam break of a one-dimensional flow.

Coupling Dispersive Shallow Water Models by Deriving Asymptotic Interface Operators

HAL (Le Centre pour la Communication Scientifique Directe), Nov 14, 2022

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

Water Waves

The goal of this special issue is to provide an overview of recent progress in the area of numeri... more The goal of this special issue is to provide an overview of recent progress in the area of numerical methods and applications for ocean waves in the coastal environment, to identify current challenges and to present and discuss approaches for performing accurate predictions of nonlinear and dispersive water waves and our ability to understand and predict impacts on coastal structures and urban areas. Over 1.6 million kilometers of coastlines occur on the earth's surface. These areas are subject to hazards created by a range of natural events, such as earthquakes and hurricanes which are a source for large waves and have a negative economic and social impact on the affected areas. In recent decades, mathematical and numerical modeling of free surface flows in realistic coastal environments has become an active research field and has been developed to the point where it is possible to provide operational information. In many situations, simulations with numerical coastal models represent a necessary complement to laboratory experiments for both site assessment and coastal design. Numerical modeling has also become an essential complement to experimental investigations at small scales, due to the potential of providing a more complete description of the underlying physics. Significant research efforts have been put into advancing the understanding of important coastal processes, such as wave propagation, shoaling, diffraction, refraction, wave breaking and run-up over the shoreline; see for example [1, 14] and references therein. These advances improve our ability to understand and predict impacts on coastal structures and urban areas. In this framework, a review of some of the most relevant modeling approaches and numerical discretization techniques can be found in [15]. The collected papers of this issue are directed to discuss modern developments and trends in the accurate numerical modeling of free surface flows. We can divide the B Maria Kazolea

On the Numerical Solution of Sparse Linear Systems Emerging in Finite Volume Discretizations of 2D Boussinesq-Type Models on Unstructured Grids

Water

This work aims to supplement the realization and validation of a higher-order well-balanced unstr... more This work aims to supplement the realization and validation of a higher-order well-balanced unstructured finite volume (FV) scheme, that has been relatively recently presented, for numerically simulating weakly non-linear weakly dispersive water waves over varying bathymetries. We investigate and develop solution strategies for the sparse linear system that appears during this FV discretisation of a set of extended Boussinesq-type equations on unstructured meshes. The resultant linear system of equations must be solved at each discrete time step as to recover the actual velocity field of the flow and advance in time. The system’s coefficient matrix is sparse, un-symmetric and often ill-conditioned. Its characteristics are affected by physical quantities of the problem to be solved, such as the undisturbed water depth and the mesh topology. To this end, we investigate the application of different well-known iterative techniques, with and without the usage of preconditioners and reord...

Sensitivity analysis for two wave breaking models used by the Green-Naghdi equation

HAL (Le Centre pour la Communication Scientifique Directe), Jan 11, 2021

Wave propagation breaking, and overtoping on a 2D reef : a comparative evaluation of numerical codes for tsunami modelling

Dans le cadre du projet de recherche français TANDEM dédié à la modélisation de tsunamis, une sér... more Dans le cadre du projet de recherche français TANDEM dédié à la modélisation de tsunamis, une série de tests a été mise enplace concernant les différentes étapes d'un tsunami : la génération, la propagation et l'inondation. Les résultats obtenus par cinq codessont présentés ici. Chacun d'eux utilise les équations de Boussinesq moyennées sur la profondeur et les équations de Naver-Stokes entrois dimensions adaptées à la modélisation de tsunamis. Ces codes sont évalués sur un écoulement impliquant la propagation, lasubmersion, et la réflexion des vagues sur un récif en deux dimensions. Une comparaison est effectuée à partir de données expérimentalesprovenant du laboratoire d'Hinsdale (O.H Hinsdale Wave Research Laboratory, Oregon State University, OSU, voir Roeber et al.,2010 etRoeber et Chung, 2012).In the framework of the French research project TANDEM dedicated to tsunami modelling, a series of benchmarks has been set up, addressing the various stages of a tsunami e...

Simulation de la propagation et du déferlement d’une vague et de l’inondation d’unrèclif 2D: évaluation comparative des codes numérique pour la modélisation des tsunamis

In the framework of the French research project TANDEM dedicated to tsunami modelling, a series o... more In the framework of the French research project TANDEM dedicated to tsunami modelling, a series of benchmarks has been set up, addressing the various stages of a tsunami event: generation, propagation, run-up and inundation. We present here the results of five codes, involving both depth-averaged Boussinesq and fully 3D Navier-Stokes equations, aimed at being applicable to tsunami modelling. The codes are evaluated on a flow involving propagation, run-up, overtopping and reflection of the waves on two-dimensional reefs, and compared with the experimental data produced from a set of laboratory experiments carried out at the O.H. Hinsdale Wave Research Laboratory, Oregon State University (OSU, see Roeber et al., 2010 and Roeber and Chung, 2012).Dans le cadre du projet de recherche français TANDEM dédié à la modélisation de tsunamis, une série de tests a été mise enplace concernant les différentes étapes d'un tsunami : la génération, la propagation et l'inondation. Les résultat...

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

Water Waves

We consider the issue of wave-breaking closure for the well known Green-Naghdi model and attempt ... more 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 setup. 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].

Well-balanced shock-capturing hybrid finite volume-finite difference schemes for Boussinesq-type models

A low dispersion finite volume/element method for nonlinear wave propagation, breaking and runup on unstructured meshes

HAL (Le Centre pour la Communication Scientifique Directe), Oct 25, 2021

We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to sol... more We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to solve a fully-nonlinear and weakly-dispersive depth averaged wave propagation model. The FV method is used to solve the underlying hyperbolic shallow water system, while a standard P 1 finite element method is used to solve the elliptic system associated to the dispersive correction. We study the impact of several numerical aspects: the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the well-posedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H 1. We show, based on both heuristic and strong numerical evidence, that numerical dissipation plays a major role in stabilizing the coupled method, and not only providing convergent results, but also providing the expected convergence rates. Finally, the full mode, coupling a wave breaking closure previously developed by the authors, is thoroughly tested on standard benchmarks using unstructured grids with sizes comparable or coarser than those usually proposed in literature.

Numerical study of wave conditions for the old Venetian harbor of Chania in Crete, Greece

In this work we present a numerical study of the long wave conditions induced in the old Venetian... more In this work we present a numerical study of the long wave conditions induced in the old Venetian Harbor of Chania (in the island of Crete, Greece) using two models. The fully nonlinear-weakly dispersive COULWAVE code and the weakly nonlinear-weakly dispersive TUCWave code. The two models are used to determine the resonant frequencies, amplitudes and modes of the entire harbor basin. The presented results are compared and discussed

New Software and Platforms - SLOWS

Wave breaking for Boussinesq-type models using a turbulence kinetic energy model

This work aims at providing a simple and improved description of wave breaking in the framework o... more This work aims at providing a simple and improved description of wave breaking in the framework of Boussinesq type modelling. In particular, we evaluate the coupling of both a weakly and a fully non-linear Boussinesq system with a turbulence model. We reformulate an evolution model for the turbulent kinetic energy, initially proposed by Nwogu, and evaluate its capabilities to provide sufficient dissipation in breaking regions. We also compare this dissipationto the one introduced by the numerical discretization.

Advanced Numerical Simulation of Near-Shore Processes by Extended Boussinesq-Type Models on Unstructured Meshes

European Consortium for Mathematics in Industry, 2014

A numerical code that employs a higher-order finite volume scheme on unstructured meshes for appr... more A numerical code that employs a higher-order finite volume scheme on unstructured meshes for approximating enhanced Boussinesq-type equations is presented. The objective of this study is to further investigate wave propagation over complex bathymetries using the developed code and to present an approach for the parallelization of the resulted code, along with preliminary numerical results.

A database of validation cases for tsunami numerical modelling

This work has been performed by a French national consortium within the framework of the national... more This work has been performed by a French national consortium within the framework of the national project Tandem, with aim to improve knowledge about tsunami risk on the French coasts. Workpackage #1 of this project was the opportunity to build a database of benchmark cases to assess the capabilities of 18 codes, solving various set of equations with different numerical methods. 14 test cases were defined from the existing literature with validation data from reference simulations, theoretical solutions or lab experiments. They cover the main stages of tsunami life: 1) generation, 2) propagation, 3) run-up and submersion, and 4) impact. For each case several of the numerical codes were compared in order to identify the forces and weaknesses of the models, to quantify the errors that these models may induce, to compare the various modelling methods, and to provide users with recommendations for practical studies. In this paper, 3 representative cases are selected and presented with a...

Hybrid finite-volume/finite-element simulations of fully-nonlinear/weakly dispersive wave propagation, breaking, and runup on unstructured grids

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more 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. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Hybrid finite-volume/finite-element simulations of fully-nonlinear/weakly dispersive wave propagation, breaking, and runup on unstructured grids Andrea Gilberto Filippini, Maria Kazolea, Mario Ricchiuto

A Flexible 2D Nonlinear Approach for Nonlinear Wave Propagation, Breaking and Run up

We present a hybrid solution strategy for the numerical solution of the two-dimensional (2D) part... more We present a hybrid solution strategy for the numerical solution of the two-dimensional (2D) partial differential equations of Green-Nagdhi (GN), which simulates fully nonlinear, weakly dispersive free surface waves. We re-write the standard form of the equations by splitting the original system in its elliptic and hyperbolic parts, through the definition of a new variable, accounting for the dispersive effects and having the role of a non-hydrostatic pressure gradient in the shallow water equations. We consider a two-step solution procedure. In the first step we compute a source term by inverting the elliptic coercive operator associated to the dispersive effects; then in a hyperbolic step we evolve the flow variables by using the non-linear shallow water equations, with all non-hydrostatic effects accounted by the source computed in the elliptic phase. The advantages of this procedure are firstly that the GN equations are used for propagation and shoaling, while locally reverting ...

Mathematical and computational modeling for the generation and propagation of waves in marine and coastal environments

Στο ϑαλάσσιο περιβάλλον εξελίσσεται ταυτόχρονα ένα πλήθος κυµατικών ϕαινοµένων,αρκετά από τα οποί... more Στο ϑαλάσσιο περιβάλλον εξελίσσεται ταυτόχρονα ένα πλήθος κυµατικών ϕαινοµένων,αρκετά από τα οποία βρίσκονται σε ουσιώδη σύζευξη µεταξύ τους. Η προσοµοίωσητης γένεσης και διάδοσης των κυµατισµών και η ακριβής περιγραφή τωνµετασχηµατισµών που υφίστανται στις παράκτιες περιοχές είναι απαραίτητη σεσχέση µε τον σχεδιασµό των ϑαλάσσιων κατασκευών, την ασφάλεια καθώς και τηνπρόβλεψη της εξέλιξης του προφίλ της ακτογραµµής. ΄Ενα από τα πιο ενδιαφέροντακαι ενεργά πεδία έρευνας, τις τελευταίες δεκαετίες είναι η µαθηµατική και αριθµητικήµοντελοποίηση των επιφανειακών κυµατισµών β αρύτητας. Αυτό αποτελεί και τοαντικείµενο µελέτης της παρούσας εργασίας. Τα µοντέλα που χρησιµοποιούνταιευρέως τα τελευταία χρόνια, για αυτό το σκοπό, είναι τα µοντέλα µέσου βάθους,µε το πιο γνωστό από αυτά να είναι οι µη γραµµικές εξισώσεις ρηχών υδάτων(NSWE). Οι εξισώσεις αυτές είναι ικανές να µοντελοποιήσουν µερικά σηµαντικάϕαινόµενα όπως η αναρρίχηση των κυµάτων σε ακτές αλλά δεν είναι κατάλληλες γιανερά µέσου η ...

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

European Journal of Mechanics - B/Fluids, 2018

The application and validation, with respect to the transformation, breaking and run-up of irregu... more 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.