The homogeneous cooling state for a binary mixture of inelastic hard spheres is studied using the Enskog kinetic theory. In the same way as for the one-component fluid, we propose a scaling solution in which the time dependence of the distribution functions occurs entirely through the temperature of the mixture. A surprising result is that the (partial) temperatures of each species are differen...

Model equations for the description of chemical reactions of dissociation and recombination through a transition state constitute necessarily singular perturbation problems because of the very short lifetime of the excited molecules, compared to all other characteristic times. Asymptotic solutions are derived and tested versus an accurate numerical solution by resorting to different expansion a...

We present the first numerical solutions of a kinetic theory description of selfsustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. ...

Starting from the molliied version of the Enskog equation for a hard-sphere uid, a grid-free algorithm to obtain the solution is proposed. The algorithm is based on the nite pointset method. For illustration, it is applied to a Riemann problem. The shock-wave solution is compared to the results of Frezzotti and Sgarra where a good agreement is found.

Methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equations are presented. Featured methods include the Chapman-Enskog expansion, Grad’s moment method, and the author’s order of magnitude method. The resulting macroscopic equations are compared and discussed by means of simple problems, including linear stability, shock wave structures, and Couette flow.

The paper presents a systematic derivation of macroscopic equations for freeway traffic flow from an Enskog-like kinetic approach. The resulting fluid-dynamic traffic equations for the spatial density, average velocity, and velocity variance of vehicles are compared to equations, which can be obtained from a microscopic force model of individual vehicle motion. Simulation results of the models ...

A general approach to the construction of discrete equilibrium distributions is presented. Such distribution functions can be used to set up Kinetic Schemes as well as Lattice Boltzmann methods. The general principles are also applied to the construction of Chapman Enskog distributions which are used in Kinetic Schemes for compressible Navier Stokes equations.