Coastal flow models and boundary conditions

Liste des Contributions

3. Large time stability issues for finite difference schemes (session 1)

Jean-François Coulombel (Institut de Mathématiques de Toulouse)

24/10/2022 14:00

We prove generalized Gaussian bounds for the large time behavior of finite difference approximations of the transport equation. The goal of the talk is to review the connection with the central limit theorem in probability theory, some history of the problem and to present the general methodology leading to sharp estimates for the Green's function. The talk is based on a joint work with Grégory Faye.

4. Derivation and justification of shallow water models for surface gravity waves and stratified flows (session 1)

Vincent Duchêne (CNRS & Université de Rennes 1)

24/10/2022 16:00

We shall discuss how standard models in oceanography can be rigorously justified as asymptotic models, here in the shallow water regime, focusing on the general strategy and mathematical tools which are involved. Most of the discussion will be devoted to the justification of the Saint-Venant system for homogeneous potential flows with a free surface. Yet going through this somewhat standard...

11. Waves - floating structure interactions in Boussinesq regime

Dr Geoffrey Beck (INRIA Rennes)

25/10/2022 09:00

In the context of nearshore wave energy facilities, we have tackled, with David Lannes and Lisl Weynans, the interaction of waves with a floating structure immersed in a 2D fluid. Some difficulties come from the presence of several surfaces: the surface of the sea and the contact surface between the structure and the fluid. The horizontal plane is decomposed into two regions: the exterior...

10. Numerical simulation of shallow-water and floating object nonlinear interactions

M. Ali Haidar (Université de Montpellier)

25/10/2022 09:50

In this work, a novel numerical algorithm is introduced for the study of nonlinear interactions between free-surface shallow-water flows and a partly immersed floating object. The object's motion may be either prescribed, or computed as a response to the hydrodynamic forcing. Away from the object, the nonlinear hyperbolic shallow-water equations are used, while the description of the flow...

9. Quelques aspects mathématiques et numériques dans la représentation des interactions océan-atmosphère

Prof. Eric Blayo (Université Grenoble Alpes)

25/10/2022 11:20

Les interactions océan-atmosphère (OA) jouent un rôle important dans de nombreux phénomènes, tels que cyclones tropicaux ou dynamique du climat. La représentation de ces interactions au sein d’un système de modélisation OA consiste principalement à évaluer les flux échangés entre les deux milieux, et à les imposer à l’interface air-mer.
Cet exposé abordera quelques questions mathématiques...

7. Seismic waves: a unique source of information on glaciers and landslides (session 1)

Prof. Anne Mangeney (Université Paris Cité)

25/10/2022 14:00

I will show here how the coupling between numerical modelling of glaciers and landslides associated with the analysis of the generated seismic waves makes it possible to recover unique information on the source processes. These waves provide a unique tool to constrain the models by providing detailed information on the dynamics of landslides and iceberg calving. This approach allows...

8. Seismic waves: a unique source of information on glaciers and landslides (session 2)

Prof. Anne Mangeney (Université Paris Cité)

25/10/2022 16:00

I will show here how the coupling between numerical modelling of glaciers and landslides associated with the analysis of the generated seismic waves makes it possible to recover unique information on the source processes. These waves provide a unique tool to constrain the models by providing detailed information on the dynamics of landslides and iceberg calving. This approach allows...

12. Sharp regularity results for solutions of boundary value problems

Corentin Audiard (Sorbonne Université)

26/10/2022 09:00

We study the well-posedness of initial boundary value problems for the linear Schrödinger equations on a half space. The boundary data lie in a (allegedly optimal) Bourgain type Sobolev space, which allows to include Neuman and transparent boundary conditions in the analysis. Strichartz estimates (in $L^2$) are obtained thanks to an explicit solution formula. In the case of Dirichlet boundary...

13. Nonlinear damping vs. formation of singularities

M. Aric Wheeler (Indiana University)

26/10/2022 09:50

We explore the boundaries of damping estimates by comparing and contrasting two closely related models of combustion, the Majda and ZND models. We show that singularities form in the unweighted Lipschitz norm in finite time on both sides of the shock for both models, extending classical results of John and Liu to suitable variable coefficient systems. On the other hand, we show some energy...

14. Smooth branches of travelling waves for the 2D Nonlinear Schrödinger equation

Dr David Chiron (Université Côte d'Azur)

26/10/2022 11:20

We shall present some results on the existence of smooth branches of travelling waves for the 2D nonlinear Schrödinger equation parametrized by the speed. In the limit of small speed (joint works with E. Pacherie), the travelling wave has two well separated vortices and we prove that these are the only minimizers of the energy for fixed momentum. In the limit where the speed is close to the...

5. Large time stability issues for finite difference schemes (session 2)

Gregory FAYE

26/10/2022 14:00

Following session 1, we shall present some sharp estimates for the Green's function of finite difference schemes that approximate the incoming transport equation on a half-line. The stability analysis relies on a precise description of the possible eigenvalues arising from the interplay between the finite difference scheme and the numerical boundary conditions. The talk is based on a joint...

6. Derivation and justification of shallow water models for surface gravity waves and stratified flows (session 2)

Vincent Duchêne (CNRS & Université de Rennes 1)

26/10/2022 16:00

We shall discuss how standard models in oceanography can be rigorously justified as asymptotic models, here in the shallow water regime, focusing on the general strategy and mathematical tools which are involved. Most of the discussion will be devoted to the justification of the Saint-Venant system for homogeneous potential flows with a free surface. Yet going through this somewhat standard...

17. Numerical proof of stability for finite difference schemes in a finite space domain

M. Pierre Le Barbenchon (Université Rennes 1)

27/10/2022 09:00

The goal of this talk is to study the stability of finite differences schemes for scalar hyperbolic initial boundary value problem. It is based on the GKS theory (introduced by Gustafsson, Kreiss and Sundström) and it deals with the Kreiss-Lopantinskii determinant. We will use complex analysis and geometric consideration to find zeros of this determinant and conclude on the stability of the scheme.

16. PML methods for mixed hyperbolic-dispersive equations

Dr Maria Kazakova (Université Savoie Mont Blanc)

27/10/2022 09:50

The classical PML approach is first applied to the linearised Korteweg-de Vries equation. These equations are not always stable, the main obstruction being the classical condition found in the literature on PMLs that we recover in our analysis. We introduce two alternative strategies to design absorbing boundary conditions. We start from studying hyperbolic relaxation of the Korteweg-de Vries...

15. On the "projection" structure of the Green-Naghdi equations

Martin Parisot (Inria)

27/10/2022 11:20

Many reduced models of the water wave equations, in particular the Green-Naghdi equations, can be presented as a "projection" of the shallow water equations onto a set of admissible functions. We will see why we use quotation marks for this property, and how to use it to its advantage for many numerical and modeling problems (entropic stability, boundary conditions, balanced, HPC, coupling,...