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Vassilios, Dougalis  WPI Seminarroom C 714  Mon, 21. Sep 09, 9:30 
"GalerkinFinite Element Methods for Boussinesq systems". Part 1  
We consider a family of systems of Boussinesq type due to Bona, Chen and Saut approximating the Euler equations of surface water wave theory, and modeling twoway nonlinear dispersive long wave propagation. We review recent progress on the theory of wellposedness of initial and initialboundaryvalue problems for these systems in two space dimensions. We approximate the systems by fully discrete numerical schemes using Galerkin  finite element methods for the spatial discretization, and analyze the stability and convergence of these schemes. The numerical methods are used as exploratory tools in a series of numerical experiments simulating various complex twodimensional flows. We also study, by numerical means, interactions of solitarywave solutions of these systems in one space dimension, including headon and overtaking collisions, and interactions of solitary waves with the boundaries.  

Vassilios, Dougalis  WPI, Seminarroom C 714  Mon, 21. Sep 09, 11:00 
"GalerkinFinite Element Methods for Boussinesq systems". Part 2  

Céline AcaryRobert  WPI, Seminarroom C 714  Mon, 21. Sep 09, 14:00 
"A powdersnow avalanche impact on protecting structures"  
In the mountain regions snow avalanches represent a major natural hazard for both life and property. In the present study we focus mainly on two aspects of the avalanche simulation problem. Namely, the first part of the talk is devoted to some twofluid models of a powdersnow avalanche. After a brief review of existing approaches we present a model which has a property to be consistent in the kinetic energy. Numerical results on an avalanche flow around an obstacle are presented.  

Médéric, Argentina  WPI, Seminarroom C 714  Mon, 21. Sep 09, 15:30 
"The Inertial Lubrication Theory"  
Thin ﬂuid ﬁlms can have surprising behaviors depending on the boundary conditions enforced, the energy input, and the speciﬁc Reynolds number of the ﬂuid motion. Here we study the equations of motion for a thin ﬂuid ﬁlm with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a suﬃciently high input of energy. We derive the minimal set of equations containing inertial eﬀects in this strongly dissipative regime.  

Vassilios, Dougalis,  WPI, Seminarroom C 714  Tue, 22. Sep 09, 9:30 
"GalerkinFinite Element Methods for Boussinesq systems". Part 3  

Vassilios, Dougalis  WPI, Semianrroom C 714  Tue, 22. Sep 09, 11:00 
"GalerkinFinite Element Methods for Boussinesq systems". Part 4  

Gisclon, Marguerite  WPI, Seminarroom C 714  Tue, 22. Sep 09, 14:00 
"Velocity and energy relaxation in twophase flows"  
Abstract: The problems of wave impact, wave breaking and other violent phenomena necessitate taking into account the compressibility of the airwater mixture. To meet these practical needs, F. Dias, D. Dutykh and J.M. Ghidaglia proposed recently a simple single velocity, single energy twophase model [Dias et al., 2009]. Properties and performance of this socalled fourequations model have already been discussed in the literature.  

Dutykh,Denys  WPI, Seminarroom C 714  Tue, 22. Sep 09, 15:30 
"Tsunami wave energy"  

Mitsotakis, Dimitrios  WPI, Seminarroom C 714  Wed, 23. Sep 09, 9:30 
"On some finite volume schemes applied to nonlinear dispersive wave equations"  
We apply and analyse some finite volume schemes to several Boussinesq type systems of water wave theory. A comparison with other numerical methods such as pseudospectral, standard Galerkin and discontinuous Galerkin is made. Special attention is given to the runup of long waves on a plane beach. Various algorithms are considered. Validation by experimental data is presented for the headon collision of solitary waves, wet dam break problem and the runup of nonbreaking and breaking solitary waves on a plane beach.  

Clamond, Didier  WPI, Seminarroom C 714  Wed, 23. Sep 09, 11:00 
"Direct Simulation of Surface Gravity Waves"  
For the simulation of fully nonlinear surface gravity waves, a fast, accurate and robust numerical scheme is presented. The method is based on a boundary integral formulation,rewritten in a convenient form, together with a pseudospectral spatial scheme and a highorder temporal one. Various applications are presented.  

Katsaounis, Theodoros  WPI, Seminarroom C 714  Wed, 23. Sep 09, 14:00 
"Relaxation Schemes for the shallow water equations"  
We present a class of relaxation schemes for the shallow water equations. These schemes are based on classical relaxation models for conservation laws. We consider finite volume as well as finite element spatial discretizations combined with TVD RungeKutta time stepping mechanisms. Numerical results are presented for several benchmark test problems.  

Chhay, Marx  WPI, Seminarroom C 714  Wed, 23. Sep 09, 15:30 
"Invariant numerical schemes"  
The Partial Differential Equations (PDE) which naturally arise in Fluid Mechanics problems admit transformations conserving the whole set of solutions. They form the socalled symmetry group of the PDE. Usually, this group contains some important physical properties of the system expressed in the language of symmetries. It appears natural to expect numerical methods to preserve at least some of symmetry transformations of the continuous system. In this talk, we present various approaches for the construction of such invariant schemes. Some comparisons are made and good performance of invariant schemes is highlighted.  

Milewski. Paul  WPI, Seminarroom C 714  Thu, 24. Sep 09, 9:30 
"Models for deepwater capillarygravity waves: solitary waves and singularities"  
Deepwater capillarygravity waves on the surface of a threedimensional fluid exhibit a very interesting range of behavior  including lump or wavepacket solitary waves  and are also numerically challenging. We shall describe some of the models we have put forth and the numerical methods used to compute solutions. We present computations of the dynamics of waves showing interesting inelastic solitary wave collisions and, in some models, computations pointing to a wavebreaking singularity.  

Saut, JeanClaude  WPI, Seminarroom C 714  Thu, 24. Sep 09, 11:00 
"A model for large amplitude internal waves"  
After recalling briefly its derivation from the twolayer system with a rigid lid, we present theoretical and numerical results on a model for large amplitude internal waves which in some sense extends to internal waves the classical SaintVenant ("Shallow water") system for surface waves. This model turns out to be nonlocal in two horizontal dimensions due to the rigid lid assumption.  

Marc, Francius  WPI, Seminarroom C 714  Thu, 24. Sep 09, 14:00 
"Models for wind effects in DNS of Surface Gravity Waves"  
Nowadays, there exist different mathematical formulations to study the dynamics of fully nonlinear freesurface waves. On the other hand, there have been a growing interest in understanding the wind effects on different nonlinear surface waves phenomena, like BenjaminFeir instability and the formation of extreme "freak" waves. As we shall see, no definitive conlusions about the wind effects in fully nonlinear simulations have been reached, owing to the complexity of the windwaves interactions problem. In this study, we use a Higher Order Spectral (HOS) method to simulate numerically the nonlinear evolution of gravity waves in the presence of a turbulent airflow above the waves. After a description of the physics involved in the problem of windwaves interactions, we present various approaches to introduce aerodynamic drag forces in DNS of surgace gravity waves. It will be assumed that the wave motions are "weakly viscous". Thus, we can use a quasipotential approximation to incorporate weak dissipation effects in our fully nonlinear simulations. Although the coupling of the wave with the airflow, via the pressure surface field, is usually based on the linear approach for the windwave interaction problem, we will present methods to go beyong the linear theory of windwave interactions. These models of wind effects are such that nonlinearity in the waves can affect the forcing during the course of the evolution.  

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