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 introduced (moments of the Boltzmann collision int scattering rates). They are treated as independent variables rather than as infinite series. This approach gives the complete account of rates of scattering processes. T equations for scattering rates are obtained (the second hydrodynamic chain), simil usual moment chain (the first hydrodynamic chain). Various examples of the closu first, of the second, and of the mixed hydrodynamic chains are considered for the ha model. It is shown, in particular, that the complete account of scattering processes l renormalization of transport coefficients. The method gives the explicit solution for the closure problem, provides thermo properties of reduced models, and can be applied to any kinetic equation thermodynamic Lyapunov function. r 2005 Elsevier B.V. All rights reserved.