Modeling and Simulation of Thick Sprays through Coupling of a Finite Volume Euler Equation Solver and a Particle Method for a Disperse Phase

We present here the principles of the coupling between an efficient numerical method for hyperbolic systems, namely the FVCF scheme (that is, a finite volume scheme used in the context of non conservative equations arising in multiphase flows), on the one hand; and a particle method for the Vlasov-Boltzmann equation of PIC-DSMC type (that is, in which macroscopic quantities are computed in each cell by adding quantities attached to the particles, and where integrals are computed thanks to a random sampling), on the other hand. Numerical results illustrating this coupling are shown for a problem involving a spray (droplets inside an underlying gas) in a pipe which is modeled by a 1D fluid-kinetic system

Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves

We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions and the possible profiles of the traveling waves solutions of semi-linear Schr\"odinger equations.Comment: 23 page

Quantum Zakharov Model in a Bounded Domain

We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This result confirms the conclusion recently made in physical literature concerning the absence of collapse in the quantum Langmuir waves. In the dissipative case the existence of a finite dimensional global attractor is established and regularity properties of this attractor are studied. For this we use the recently developed method of quasi-stability estimates. In the case when external loads are $C^\infty$ functions we show that every trajectory from the attractor is $C^\infty$ both in time and spatial variables. This can be interpret as the absence of sharp coherent structures in the limiting dynamics.Comment: 27 page

Singularization of sloshing impacts

Marine and Transport TechnologyMechanical, Maritime and Materials Engineerin