Related papers: A consistent BGK model with velocity-dependent col…
We introduce a ``two-particle factorization'' condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide…
For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and…
We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a…
The hypothesis of ``molecular chaos'' is shown to fail when applied to spatially inhomogeneous evolution of a low-density gas, because this hypothesis is incompatible with reduction of interactions of gas particles to ``collisions''. The…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674…
We report an experimental study of a dilute "gas" of inelastically colliding particles excited by vibrations in low gravity. We show that recording the collision frequency together with the impulses on a wall of the container gives access…
The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model…
We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range…
This paper considers a kinetic equation for an unbounded two-dimensional single species point vortex system. No axisymmetric flow is assumed. Using the kinetic theory based on the Klimontovich formalism, we derive a collision term…
We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently…
The multi-scale flow mechanism is crucial for force and heat loaded on near-space and reentry vehicles, the control of spacecraft by thrusters, the propelling and cooling of MEMS, etc. Since the continuum flow and rarefied flow often exist…
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…
The Boltzmann kinetic equation for dilute granular suspensions under simple (or uniform) shear flow (USF) is considered to determine the non-Newtonian transport properties of the system. In contrast to previous attempts based on a…
We establish global existence of mild solutions to the BGK model proposed by Bouchut [J. Stat. Phys., 95, (1999), 113--170] under the minimal assumption of finite kinetic entropy initial data. Moreover we rigorously derive a kinetic entropy…
In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservative due to mutual interaction between species. In…
The gas-kinetic scheme (GKS) provides high computational efficiency and accuracy for continuum flow simulations but is unable to reliably capture rarefaction effects. In contrast, although the discrete velocity method (DVM) is better suited…
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…