Narrow Results

Lattice-based models have been attracting much interest in recent years and have been applied to many complex systems. The derivation of large scale dynamical equations of lattice-gas models as well as lattice-Boltzmann models was based on the belief that only the physically interesting quantities (mass, momentum and energy) are conserved. Staggered invariants in lattice-gas models were found in 1988 and there have been no efficient methods to eliminate these invariants. In this paper, we will first discuss the existence of staggered invariants, then we propose to use fractional propagation as an effective way of suppressing these undesired invariants. Numerical simulations will be used to confirm the theory and to show the improvement of computations.

In this paper, we present numerical results of finite size effect in lattice-BGK models applied to liquid-gas phase transitions in one dimension. Several "pseudo-potentials" are used in simulations and the lattice size varies from 4 lattice sites to 4096 sites. Power law scaling is found and simple mean-field theory is used to explain the numerical finding.

We consider a discrete kinetic approximation of the isentropic Euler equations, and establish the local convergence of the solutions of these relaxation systems to those of the hydrodynamic equations in the hyperbolic limit. We rely on modulated entropy methods and cover the time interval in which the latter admits smooth solutions.

The steady shock–wave problem in a chemically reacting gas mixture is addressed at the kinetic level. A consistent BGK model is employed for constructing the shock profiles, and preliminary numerical results are presented.