Kinetic modeling of the transport of dust particles in a rarefied atmosphere (Q2905297)

The authors propose a new kinetic model to describe the interactions between a rarefied gas and dust particles. The dust particles are assumed to be large with respect to the gas molecules, suggesting the replacement of the usual Boltzmann kernel for hard spheres by a random Boltzmann kernel corresponding to a diffuse reflection boundary condition on the surface of the dust particles for gas/dust collisions. On the short time-range, the authors consider that dust/dust collisions can be neglected.NEWLINENEWLINEFor the sake of numerical computations, they also introduce two coupled Vlasov-Boltzmann systems obtained as the first term in an asymptotic expansion in two different regimes for which the ratio (mass of gas molecule)/(mass of dust particle) goes to zero and grazing collisions are dominant for the dust particles (see [\textit{R. Alexandre} and \textit{C. Villani}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 21, No. 1, 61--95 (2004; Zbl 1044.83007); \textit{P. Degond} and \textit{B. Lucquin-Desreux}, Math. Models Methods Appl. Sci. 2, No. 2, 167--182 (1992; Zbl 0755.35091); \textit{L. Desvillettes}, Transp. Theory Stat. Phys. 21, No. 3, 259--276 (1992; Zbl 0769.76059)]). Such systems are cheaper to implement numerically and yield good approximations in the situations they consider. Explicit numerical simulations refer to safety studies for ITER tokamaks regarding various hazards produced by a mobilization of dust particles extracted from the surface of the vessel due to air leaks (the so-called LOVA, loss of vacuum accident). Parameters are realistic when ITER is turned off, at standard temperature and pressure conditions (see the reference [\textit{J. Zhang} et al., ``Numerical modeling of ionian volcanic plumes with entrained particulates'', Icarus 172, No. 2, 479--502 (2004; \url{doi:10.1016/j.icarus.2004.06.016})] cited in the text for possible application to a different context).