We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of the interaction strength, the competition between stable and unstable regions results in a short-ranged disordered fluid pattern with sharp density contrasts. These disordered configurations contrast with phase-separation scenarios typically observed in binary fluids. The present results indicate that frustration can be modelled within the framework of a suitable one-body effective Boltzmann equation. The lattice implementation of such an effective Boltzmann equation may be seen as a preliminary step towards the development of complementary/alternative approaches to truly atomistic methods for the computational study of glassy dynamics.

We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature TF. We examine the transition from the collisionless to the collisional regime down to T = 0.2 TF and find a good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular, we observe a hitherto unreported effect, namely, the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.

By improving a one-dimensional model proposed by De Fabritiis, Mancini, Mansutti and Succi in 1998, we develop a simple reaction model for liquid-solid phase transitions in the context of the lattice Boltzmann method with enhanced collisions.Calculations for a two-dimensional test problem of gallium melting and for a two-dimensional anisotropic growth of dendrites are presented and commented on.

A generalization of mesoscopic Lattice-Boltzmann models aimed at describing flows with solid/liquid phase transitions is presented. It exhibits lower computational costs with respect to the numerical schemes resulting from differential models, Moreover it is suitable to describe chaotic motions in the mushy zone.