We discuss further developments of the finite-volume lattice Boltzmann formulation on unstructured grids. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size. A theoretical argument of plausibility for such a property is presented. In addition, a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows.

A dynamic optimization strategy is presented to generate customized equations of state (EOS) for the numerical simulation of non-ideal fluids at high density ratio. While stable branches of the analytical EOS are preserved, the spinodal region is self-tuned during the simulation, in order to compensate for numerical errors caused by discretization in phase space. The employed EOS permits the readily setting of the sound speeds for the gas and liquid phases, thus allowing stable simulation with high density (1 : 10 to 1 : 1000) and compressibility ratios (250 : 1–25000 : 1). The present technique is demonstrated for lattice Boltzmann simulation of (free-space) multiphase systems with flat and circular interfaces.

It is shown that the cooperation between short and mid range attraction in Lattice Boltzmann (LB) models with multi-range pseudo-potentials, permits the achievement of phase-separation at liquid/vapor density ratios in excess of 1 : 500, nearly an order of magnitude above the current limits of standard single-range LB models. Inspection of the density configurations reveals that this favourable behaviour results from a sizeable reduction of spurious currents near the liquid/vapour interface. The aforementioned enhancement of the density ratio is obtained at virtually the same computational cost of the standard single-range models. As a consequence, the present results may open the way to a broader spectrum of LB applications, involving the dynamics of complex phase-separating flows with large density ratios.

Further research on both theoretical and practical aspects of a previously defined finite-volume formulation to integrate the Lattice Boltzmann equation (LBE) on unstructured grids is presented. Moreover, additional explicit schemes for time discretisation are proposed. The method is tested on an impulsively started channel flow with the aim of exactly locating solid boundaries. Cavity flow simulations are used to measure the inaccuracies due to compressibility, grid and time discretisation effects. Finally, the proposed method has been tested against a laminar flow over a backward facing step in order to assess the effectiveness of open outlet boundary treatment.