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Samer Fadel Israwi

Associate professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: App. Math and Scien. Calcu.
Interests: READ-FOOTBALL-CINEMA.
Skills: WRITING A POEM.

Teaching 6 Taught Courses
(2014-2015) GEOL 311 - Differential Equations

BS Petroleum Geology

(2014-2015) Math 171 - Mathematics (analysis)

BS Earth and life sciences

(2014-2015) Math 171 - Mathematics (analysis)

BS Earth and life sciences

(2014-2015) Math 403 - Distribution theory

M1 Mathematics

(2014-2015) MEDP 506 - Asymptotic models in oceanography

M2 Partial Differential Equations and Numerical Analysis

(2014-2015) Math 105 - Integral Calculus

BS Mathematics

Publications 12 publications
Vincent Duchene, Samer Israwi and Raafat Talhouk A new class of two-layer Green-Naghdi systems with improved frequency dispersion Wiley, SAPM, MIT 2016

We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1 + 1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom and a rigid lid. These models are tailored to improve the frequency dispersion of the original bi-layer Green-Naghdi model, and in particular to manage high-frequency Kelvin-Helmholtz instabilities, while maintaining its precision in the sense of consistency. Our models preserve the Hamiltonian structure, symmetry groups and conserved quantities of the original model. We provide a rigorous justification of a class of our models thanks to consistency, well-posedness and stability results. These results apply in particular to the original Green-Naghdi model as well as to the Saint-Venant (hydrostatic shallow-water) system with surface tension.

Samer Israwi , Ralph Lteif, Raafat Talhouk An improved result for the full justification of asymptotic models for the propagation of internal waves AIMS 2015

We consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The aim of this paper is to show that the full justification result of the model obtained by Duchˆene, Israwi and Talhouk [SIAM J. Math. Anal., 47(1), 240–290], in the sense that it is consistent, well-posed, and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data, can be improved in two directions. The first direction is taking into account medium amplitude topography variations and the second direction is allowing strong nonlinearity using a new pseudo-symmetrizer, thus canceling out the smallness assumptions of the Camassa-Holm regime for the well-posedness and stability results.

Vincent Duchene, Samer Israwi and Raafat Talhouk A NEW FULLY JUSTIFIED ASYMPTOTIC MODEL FOR THE PROPAGATION OF INTERNAL WAVES IN THE CAMASSA–HOLM REGIME Society for Industrial and Applied Mathematics 2015

This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green–Naghdi type model in the Camassa–Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent and well-posed and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data. Moreover, our system allows one to fully justify any well-posed and consistent lower order model, and, in particular, the so-called Constantin–Lannes approximation, which extends the classical Korteweg–de Vries model to the Camassa–Holm regime.

Samer Israwi and Ayman Mourad An Explicit Solution with Correctors for the Green–Naghdi Equations SPRINGER 2014

In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green– Naghdi equations can be derived and justified when the bottom is vari- able (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dis- persive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.

Vincent Duchene, Samer Israwi and Raafat Talhouk SHALLOW WATER ASYMPTOTIC MODELS FOR THE PROPAGATION OF INTERNAL WAVES AIMS 2014

We are interested in asymptotic models for the propagation of in- ternal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidi- rectional models of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model, that we introduce and justify in the sense of consis- tency. Contrarily to earlier works, our Green-Naghdi model allows a non-flat topography, and horizontal dimension d = 2. Its derivation follows directly from classical results concerning the one-layer case, and we believe such strat- egy may be used to construct interesting models in different regimes than the shallow-water/shallow-water studied in the present work.

Samer Israwi and Raafat Talhouk Local well-posedness of a nonlinear KdV-type equation ELSEVIER 2013

In this paper, a generalized nonlinear KdV equation with time- and space-dependent coefficients is considered. We show that the control of the dispersive and “diffusion” terms is possible if we use an adequate weight function determined with respect to the dispersive and “diffusion” coefficients to define the energy. We use the dispersive properties of the equation to prove the existence and uniqueness of solutions.

Marc Durufle' and Samer Israwi A numerical study of variable depth KdV equations and generalizations of Camassa–Holm-like equations ELSEVIER 2012

In this paper we numerically study the KdV-top equation and compare it with the Boussinesq equations over uneven bottoms. We use here a finite-difference scheme that conserves a discrete energy for the fully discrete scheme. We also compare this approach with the discontinuous Galerkin method. For the equations obtained in the case of stronger nonlinearities and related to the Camassa–Holm equation, we find several finite difference schemes that conserve a discrete energy for the fully discrete scheme. Because of its accuracy for the conservation of energy, our numerical scheme is also of interest even in the simple case of flat bottoms. We compare this approach with the discontinuous Galerkin method.

Samer Israwi Derivation and analysis of a new 2D Green–Naghdi system IOPSCIENCE 2011

We derive here a variant of the 2D Green–Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard 2D Green–Naghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green–Naghdi equations. Using this property, we show that the solution of these new equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition. Finally, we prove that the new Green–Naghdi equations conserve the almost irrotationality of the vertically averaged horizontal component of the velocity.

Samer Israwi Analyse mathématique de problèmes en océanographie côtière Université de Bordeaux 2010

Nous nous étudions ici le problème d'Euler avec surface libre sur un fond non plat et dans un régime fortement non linéaire où l'hypothèse de faible amplitude de l'équation de KdV n'est pas vérifiée. On sait que, pour un tel régime, une généralisation de l'équation de KdV peut être dérivée et justifiée lorsque le fond est plat. Nous généralisons ici ces résultats en proposant une nouvelle classe d'équations prenant en compte des topographies variables. Nous démontrons également que ces nouveaux modèles sont bien posés. Nous les étudions aussi numériquement. Ensuite, nous améliorons quelques résultats sur l'existence des équations de Green-Naghdi (GN) dans le cas 1D. Dans le cas de 2D, nous dérivons et étudions un nouveau système de la même précision que les équations de GN usuelles, mais avec un meilleur comportement mathématique.

Samer Israwi Large time existence for 1D Green-Naghdi equations ELSEVIER 2010

We consider here the 1D Green-Naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves. We show that the solution of the Green-Naghdi equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition.

Samer Israwi VARIABLE DEPTH KDV EQUATIONS AND GENERALIZATIONS TO MORE NONLINEAR REGIMES m2an 2009

We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa- Holm equation) can be derived and justified [Constantin and Lannes, Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom topographies. Of course, many variable depth KdV equations existing in the literature are recovered as particular cases. Various regimes for the topography regimes are investigated and we prove consistency of these models, as well as a full justification for some of them. We also study the problem of wave breaking for our new variable depth and highly nonlinear generalizations of the KdV equations.

Samer Israwi Variable depth KDV equations and generalizations to more nonlinear regimes SMAI/CANUM 2008

We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced.

Supervision 5 Supervised Students
Variable depth KDV equations and generalizations to more nonlinear regimes

Amani Bassam Kojok
Master M2 Thesis: Partial Differential Equations and Numerical Analysis in 2015

Derivation and analysis of a new 2D Green–Naghdi system.

Bashar Sami Hussien Elkhorbatly
Master M2 Thesis: Partial Differential Equations and Numerical Analysis in 2016

EDP en océanographie

Ralph lteif
Thèse de doctorat en préparation (depuis 2013) à Grenoble en cotutelle avec l'Ecole doctorale des sciences et technologies - Universite Libanaise (Raafat. Talhouk et Samer. Israwi) , dans le cadre de Mathématiques, Sciences et technologies de l'information, Informatique , en partenariat avec LAMA - Laboratoire de mathématiques de l'Université de Savoie (Stéphane Gerbi et Christian Bourdarias.)

Dans cette thèse, nous nous intéressons au comportement d'un système composé de deux fluides non miscibles, soumis à la seule force de gravité. Un tel système est utilisé en océanographie, afin de modéliser une étendue d'eau de densité variable. Récemment et dans la littérature plusieurs au­teurs ont commencé par écrire sous forme agréable les équations d'évolution gouvernant le système. Ensuite, ils ont développé des modèles asymptotiques, dans les régimes d'eau peu profonde, où l'on suppose que la profondeur des couches de fluide est petite devant la longueur d'onde caractéristique à l'interface, et d'ondes longues, où l'on ajoute une hypothèse de petitesse des déformations à la surface et à l'interface. Le but de cette thèse est de justifier rigoureusement et d'étudier mathématiquement plusieurs modèles utilisés en océanographie. Un travail de modélisation sera également envisagé pour la généralisation de modèles physiques existants appliqués a des situations plus réalistes. La première phase de la thèse consistera à analyser rigoureusement le comportement unidirec­tionnel d 'ondes internes entre deux fluides de densités différentes afin de dériver des équations uni­directionnelles consistantes avec les modèles couplés dans plusieurs régimes fortement non-linéaires et dispersifs. Il n'existe pas à ce jour de justification rigoureuse (dérivation, existence, unicité et stabilité de la solution) pour des nombreux modèles physiques décrivant cette situation (modèle de Green-Naghdi/Green-Naghdi sous différents régimes). Un autre aspect de la thèse sera l'analyse mathématique (existence, unicité, stabilité de la solution) de problèmes environnementaux liés a l'océanographie comme le modèle de Serre/Serre a fond variable, modèle de Green-Naghdi/Green-Naghdi fond plat et variable : nous envisagerons le couplage de plusieurs modèles approchés simples .L'analyse de ce couplage sera un des points forts de cette deuxième phase.

PDE's

Sleiman Saab
Thesis of Master 2 prepared in academic year (2011-2012).

We study the asymptotic model for the water waves problem with uneven bottom.

PDE's

Nada El bardan
Thesis of Master 2 prepared in academic year 2012-2013.

We study the unidirectionnels asymptotic model for the water waves problem with flat bottom.

Languages
Arabic

Native or bilingual proficiency

English

Professional working proficiency

French

Full professional proficiency