The scientific objective of the project is to study, from a mathematical and/or numerical perspective, models of partial differential equations describing aerosols (mixtures consisting of a particle phase—such as solid impurities or droplets—suspended in a gas). These models are based on kinetic theory, which describes systems consisting of a large number of elementary particles at the mesoscopic scale (between the microscopic and macroscopic scales) in terms of their density function in phase space. By letting various small physical parameters (the Knudsen number, the mass ratio between a gas molecule and a particle, the Mac number, etc.) toward 0, we can obtain various asymptotic models, such as the Euler-Vlasov model [2] (fluid-kinetic) or the Maxwell-Stefan model [3] (diffusive asymptotic), which describe the evolution of macroscopic variables: density, macroscopic velocity, and temperature. Fluid-kinetic or
Maxwell-Stefan models, which are less refined, are, however, less expensive to simulate numerically than a kinetic model.
