Workshop of the Labex CPU

Kinetic equations and applications

Bordeaux, 1st october 2013

Centre d'excellence: http://cpu.labex-univ-bordeaux.fr/en/

Organizing comitee

Stéphane Brull Stephane.Brull@math.u-bordeaux.fr




Registration

Registration is mandatory even if there is no registration fee for the conference. You can register by sending an email to Stéphane Brull .

Confirmed speaker:

Axel Klar (Kaiserslautern): Mean field hierarchies for interacting particle systems: numerical methods and applications
Asbstract: Starting from a microscopic interacting particle system, we consider mean field and related macroscopic approximations. Variants with stochastic parts, constant velocity models, maximum entropy approximations or coupling to an eikonal equation are discussed. Numerical methods for these model hierarchies include semi-Lagrangian methods for the kinetic problem and mesh free particle methods for the macroscopic equations. In particular, we investigate an asymptotic preserving particle method for diffusive limits of the macroscopic equations. These methods are applied to different applications including swarming and crowding phenomena, material flow problems and pedestrian and traffic dynamics.

Fiametta Conforto (Messine): Discontinuous travelling wave solutions in a chemically reacting mixture
Asbstract: The existence of discontinuous travelling wave (shock structure with subshock) solutions [1, 2] is studied for a mixture of four species undergoing to a bimolecular chemical reaction. The mixture is described by different closures of the reactive Boltzmann equations. Either Euler equations, either 8, 10 and 13 Grad equations [3, 4] have been used in order to state the problem and the results obtained in the different settlements are then compared.

[1] Curro C., Fusco D.: Discontinuous travelling wave solutions for a class of dissipative hyperbolic models. Rend. Mat. Acc. Lincei s. 9 16 n.1, 61{71 (2005)
[2] Mentrelli A., Ruggeri T.: Asymptotic behavior of Riemann and Riemann with structure problems for a 22 hyperbolic dissipative system. in Non Linear Hyperbolic Fields and Waves A Tribute to Guy Boillat , Greco A.M., Ruggeri T. (Eds.), Supplemento Rend. Circ. Mat. di Palermo s. II 78 , 201{226 (2006)
[3] Bisi, M., Groppi, M. and Spiga, G.: Grad's distribution functions in the kinetic equations for a chemical reaction. Continuum Mech. Thermodyn. 14 , 207{222 (2002)
[4] Bisi, M., Groppi, M. and Spiga, G.: Kinetic approach to chemically reacting gas mixtures. in Modelling and Numerics of Kinetic Dissipative Systems , Pareschi L., Russo G., Toscani G. (Eds.), Nova Science, New York, 107{126 (2005)

Roberto Monaco (Turin) : Kinetic equations for reactive mixtures: models & applications
Asbstract:The exact Boltzmann equation for a reactive mixture of gases undergoing bi-molecular reactions is introduced. A possible generalization which takes into account that the distribution functions in the kinetic equations can also depend by internal energies is then proposed and discussed. Moreover, on the side of models of the reactive Boltzmann equation, some BGK-type models for slow and fast reactions are considered as well, showing several applications at the macroscopic and mesoscopic level. Finally extension to the case of chain reactions is taken into account and some results are compared with those obtained by the so-called Quasi Steady-State Approximation (QSSA).

Florian Bernard (Bordeaux): Asymptotic preserving schemes for BGK equation with a local velocity grid approach
Asbstract: A typical feature of complex flows is the coexistence of kinetic and hydrodynamic regimes in the same field as in vacuum pump or hypersonic re-entries. In recent years, asymptotic preserving schemes for kinetic equations have been developed to ensure a smooth transition towards the hydrodynamic regime. This property has also to be preserved up to the body. A new way of enforcing the wall boundary condition on an immersed solid is presented, preserving the asymptotic limit of BGK equation towards compressible Euler equations with a good degree of accuracy (second order in space). Simulations are performed on Cartesian grids. They are very suitable for massive parallel computation and are a way to deal with the issue of high computational time requirement of kinetic equations. It is one of the main bottleneck to simulate realistic test cases. To avoid this problem, a local velocity grid approach is proposed. Test cases in 1D and 2D will be presented.

Louis Forestier-Coste (Bordeaux): A new adaptative numerical method for kinetic equations
Asbstract: We present a new deterministic numerical method for kinetic equations based on local grids for the velocity variable whereas the classical one are based on a global grid. The dynamic grids are constructed by solving a system of conservation laws and the projection of distribution functions on the new grid is obtained from interpolation procedures. Finally some test cases will be presented in a one and two dimensional setting to illustrate drawbacks and advantages of the numerical method.

Schedule

9h00-9h45 Roberto Monaco
9h45-10h15 Coffee Break
10h15-11h00 Florian Bernard
11h15-12h00 Axel Klar
14h00-14h45 Louis Forestier-Coste
15h00-15h45 Fiammetta Conforto

Confirmed Participants:

Brull Stéphane Axel Klar Fiametta Conforto
Jérôme Breil Luc Mieussens Pierre Charrier
Louis Forestier-Coste Thana Nguyen Bui Florian Bernard
Bruno Dubroca Sébastien Guisset Céline Barranger
Antoine Bourgeade Julien Mathiaud Nicolas Herouard

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