Balanced states and closure relations: the fluid dynamic limit of kinetic models

The paper is concerned with closure relations for moment hierarchies of gaskinetic systems in the uid dynamic limit. We develop the concept of balanced solutions which provides a more detailed description of kinetic solutions that the classical approaches. This allows to compare di_erent models in use like the nonlinear Boltzmann equation, its linearization, and the BGK model and their relation to the classical Navier-Stokes equations

Gelation of stochastic diffusion-coagulation systems

We investigate aerosol systems diffusing in space and study their gelation properties. In particular we work out the role of fluctuations which turn stable configurations into metastable ones, and the influence of randomly distributed sources and sinks

Approximations to the gelation phase of an aerosol

We investigate a time discretized version of the Smoluchowski coagulation equation. By means of a numerical example we prove its suitability as a basis for the efficient simulation of the transition to gelation

On a Monte Carlo scheme for Smoluchowski's coagulation equation

We propose a Monte Carlo simulation scheme for the Smoluchowski equation of aerosol dynamics and discuss its numerical efficiency

An inverse model problem in kinetic theory

The paper deals with an inverse model problem in linear kinetic theory: the identification of a density profile of a scattering medium in a slab geometry from measurement of the reflected portion of a particle flux entering the medium. We prove well-posedness of the problem and present a robust algorithm for the identification

Discretization and numerical schemes for stationary kinetic model equations

There are still many open questions concerning the relationship between (steady) kinetic equations, random particle games designed for these equations, and transitions, e.g. to fluid dynamics and turbulence phenomena. The paper presents some first steps into the derivation of models which on one hand may be used for the design of efficient numerical schemes for steady gas kinetics, and on the other hand allow to study the interplay between particle schemes and physical phenomena

Discrete kinetic models in the fluid dynamic limit

We investigate discrete kinetic models in the Fluid dynamic limit described by the Euler system and the Navier-Stokes correction obtained by the Chapman Enskog procedure. We show why reliable "small" systems can be expected only for small Mach numbers and derive a calculus for designing models for given Prandtl numbers

Macroscopic limit for an evaporation-condensation problem

We consider a rarefied gas mixture confined between two parallel walls consisting of vapor passing through the walls (evaporation, condensation), and a noncondensable which is totally reflected at the walls. Under a diffusive scaling we derive a macroscopic limit in which the noncondensable forms a well-defined boundary layer slowing down the vapor flow. The results differ substantially from others obtained with asymptotic analysis strategies. Our calculations are based on discrete velocity models

Simulation of kinetic boundary layers

The numerical transition of a kinetic boundary layer into a steady fuid field via particle simulation is studied. Several modelling aspects are treated. Criteria "measuring" the transition are proposed and studied

A numerical model for the Boltzmann equation with applications to micro flows

Given an integer lattice \mathcal{L} \subset \mathbb{R}d, we define G as the orthogonal group leaving \mathcal{L} invariant. Starting from a basic kinetic model on G we construct a collision operator on \mathcal{L} which keeps all the essential features of the classical Boltzmann collision operator. For a particular 3D lattice we demonstrate the suitability of this discrete model for the numerical simulation of rarefied flows. For several examples, e.g. in the context of micro flows, we find a good qualitative and quantitative agreement of our simulation results with test data