A lattice Boltzmann model for computing compressible two-phase flows with high density ratio

The objective of this article is to present a novel LB method to simulate compressible two-phase liquid–gas flows with two distribution functions which recovers fully compressible Navier–Stokes equations. A lattice Boltzmann framework with two distribution functions is developed in which one of the distribution functions computes the density, momentum and the temperature while the other one recovers the Cahn–Hilliard equation to capture the phase interface. The equilibrium density distribution function is chosen in such a way that the lattice Boltzmann equation recovers the Navier–Stokes equations together with the energy equation using the multiscale Chapman–Enskog expansion. The D1Q5 lattice Boltzmann model is developed to solve various test cases in one dimension including the shock tube problem. The good agreement between the numerical results and exact solutions confirms the accuracy and consistency of the method. It is also shown that the developed method is able to stably compute the compressible two-phase flows with density ratios up to 700.