On lattice Boltzmann modeling of phase transition in an isothermal non-ideal fluid
Section snippets
Introduction and background
During the past decade, the lattice-Boltzmann Equation (LBE) method (Qian et al., 1992) has been developed extensively, and has attracted significant attention in computational physics and multiphase flow modeling communities. Lying in between microscopic molecular dynamics and conventional macroscopic fluid dynamics, the LBE simulates the macroscopic complex flow behavior by dealing with the underlying micro-world. Recently, the LBE method has been shown to provide convincing results for
Lattice geometry and symmetry
Consider the lattice composed of r sublattices in d dimenstions. Each sublattice has weight wr, which are chosen to satisfy certain symmetry requirements, which will be discussed shortly. In total, the lattice has a=0, … b links, ea.
The most important properties of the lattice are related to the symmetries of the tensors:which are determined from the choice of the basic lattice directions ea.
The basic condition for standard hydrodynamic behaviour is that tensors
Numerical treatment
In the present section, new numerical schemes for solution of lattice Boltzmann equation are introduced.
Swift et al. model
It is possible to show that the model by (Swift et al., 1995) is a particular case of the model developed in the present study, if the following coefficients of the Chapman–Enskog expansion for a correction term, Eq. (39), are chosen:where p0*=p0−ρCs2 is a ‘non-ideal part’ of the equation of state and d is a space dimension. Note, that any choice of β leads to the chosen thermodynamics (pressure tensor). We have numerically proved that
Numerical results and discussion
Computational results presented in this paper are obtained by the FlowLab code. This parallel code is written in a MPI (Message-Passing Interface) standard. Currently, there are two lattice configurations available in the FlowLab: D2Q9 and D3Q15. All results presented here are obtained for a two-dimensional D2Q9 lattice.
Conclusions
In the present paper, a new lattice Boltzmann model for isothermal non-ideal fluid is introduced. The equilibrium distribution function in the BGK collision operator is split into two parts. The first part is responsible for ideal fluid behaviour (kinetic effects), while the second part is designed to represent the desired non-ideal-fluid features. Both parts of the equilibrium distribution function are approximated by the second-order Chapman–Enskog expansions in a low-Mach-number limit.
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