In the present paper a general critisicsm of kinetic equations for vehicular traac is given. The necessity of introducing an Enskog-type correction into these equations is shown. An Enskog-like kinetic traac ow equation is presented and uid dynamic equations are derived. This derivation yields new coeecients for the standard uid dynamic equations of vehicular traac. Numerical simulations for in...

A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of correlations. It is shown that renormalized transport coefficients can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation f...

Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic th...

A kinetic theory describing chemical reactions on crystal surfaces is introduced. Kinetic equations are used to model physisorbed-gas particles and chemisorbed interacting with fixed potentials colliding phonons. The phonons assumed be at equilibrium the species coupled similar atoms surface. An arbitrary number of gaseous species, surface heterogeneous considered may polyatomic. entropy introd...

The Enskog-Vlasov equation has been proven successful in capturing the complex behaviour of fluids undergoing a phase change. However, its numerical solution is computationally demanding, and this restricted studies to one- two-dimensional planar flows. In work, weighted particle scheme developed for Enskog–Vlasov spherically symmetric geometry. It shown how schemes designed Boltzmann can be ex...

We analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations—derived from the kinetic theory of gases—is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog expansion in the fast relaxation limit and es...

This article is devoted to the explanation of the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. We employ the Arrhenius constitutive model and show Hadamard instability for the linearized problem. For the nonlinear model, using an asymptotic procedure motivated by the theory of relaxation and the Chapman-Enskog expansion, we derive an effective...

The Laguerre Lattice Boltzmann (LLB) models are constructed to exactly recover integrals of the equilibrium distribution function over octants of the momentum space. In the mesoscopic formulation of the Boltzmann equation, such integrals are necessary for the implementation of diffuse reflection boundary conditions. In this paper, we consider two implementations of the force term in the LLB mod...

An instability near the transition to collective motion of self-propelled particles is studied numerically by Enskog-like kinetic theory. While hydrodynamics breaks down, the kinetic approach leads to steep solitonlike waves. These supersonic waves show hysteresis and lead to an abrupt jump of the global order parameter if the noise level is changed. Thus they provide a mean-field mechanism to ...