In this talk, we extend the derivation of the Fick-relaxation BGK model, performed in [BP S12], to a polyatomic setting. The construction of the present model is based on the introduction of relaxation coefficients and by solving an entropy minimisation problem. The distribution functions of each species are described by adding a supplementary continuous variable collecting vibrational and...

In [1] Christian Bataillon et al. have proposed a DPCM (Poisson Coupled Diffusion Model) to describe the corrosion process that occurs on the surface of steel containers in contact with the claystone formation. The model in question focuses on the development of a dense oxide layer in the region of contact between the metal and the claystone. The system formed by the layer, the metal and the...

Biofilms are accumulations of microorganisms that can be found on almost every surface, for instance as dental plaque on teeth or as an accumulation of Staphylococcus Aureus on catheters. Based on the biofilm growth model formulated by Eberl, Parker and van Loosdrecht in 2000, we formulate an implicit Euler finite–volume scheme for the degenerate–singular diffusion equation for the biomass...

When designing tokamak fusion reactors, two sets of particles need to be modeled. The electromagnetically constrained plasma, which harbors the reaction, is generally modeled as a fluid. This fluid model is coupled with a kinetic equation modeling neutral particles. When the collision rate of neutrals with the background is high, a well-defined limiting equation exists. High-dimensionality of...

Here we are interested in the boundary control problem of the small-amplitude water waves system in a rectangular tank. The model actually we used here is a fully linear and fully dispersive approximation of Zakharov-Craig-Sulem formulation constrained in a rectangle, in particular, with a wave maker. The wave maker acts on one lateral boundary, by imposing the acceleration of the fluid in the...

We consider the Boltzmann equation that models a polyatomic gas by taking into account the continuous microscopic internal energy I. In particular, we consider the kinetic system proposed by [2], which is based on the procedure of Borgnakke and Larsen [1]. We linearize the Boltzmann equation around the Maxwellian function, which represents the equilibrium distribution function. Under some...

Population dynamics can be modelled by stochastic interacting any particle systems. However their numerical approximation is time consuming so one prefers to investigate simpler macroscopic models, which are derived from the many particle systems in the mean field limit. When several species are involved, this leads to nonlocal cross-diffusion terms. We investigate a nonlocal cross-diffusion...

In this poster, we present a Hybrid Finite Volumes scheme to discretise semiconductors models. This type of finite volumes scheme [1] is devised to handle general polygonal/polyhedral meshes, alongside with anisotropic diffusion tensors. Especially, the scheme introduced here can be used in situations where the semiconductor is immersed in a magnetic field [2].

The scheme is based on the...

Perovskite solar cells (PSCs) have become one of the fastest growing photovoltaic technologies within the last few years, for example perovskite/silicon tandem cells have become more efficient than single junction silicon solar cells [1]. However, which exact physical operation mechanisms play a fundamental role within such devices is not fully understood yet. Experiments indicate that on the...

Abstract in attachment

Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This equation, modeled on the seminal Boltzmann equation, describes using a statistical physics formalism the time evolution of a gas composed of bosons or fermions....