Quasi-equilibrium closure hierarchies for the Boltzmann equation

Quasi-equilibrium closure hierarchies for the Boltzmann equation

ester, UK. In this paper, explicit method of constructing approximations (the triangle entropy is developed for nonequilibrium problems. This method enables one to treat any com nonlinear functionals that fit best the physics of a problem (such as, for example processes) as new independent variables. The work of the method is demonstrated on the Boltzmann’s-type kinet macroscopic variables are ...

Approach to equilibrium for the phonon Boltzmann equation

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved qu...

Hierarchical Moment Closure Approximation of the Boltzmann Equation

This work discusses the application of the moment method to a generic form of kinetic equations, given by the Boltzmann equation, to simplify kinetic models of particle systems. Implicit to the method of moments is an approximation of moment closure relations to close the system of equations. The main aim is to explore the opportunities, pertaining to goal-oriented adaptive modeling, presented ...

On the Trend to Global Equilibrium for Spatially Inhomogeneous Kinetic Systems: the Boltzmann Equation

Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

Xiaoyi He1,2,* and Li-Shi Luo Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Complex Systems Group T-13, MS-B213, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ICASE, MS 403, NASA Langley Research Center, 6 North Dryden Street, Building 1298, Hampton, Virginia 23681-0001 ~Received 29 April 1997; revised ma...