Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Abstract We develop a two-dimensional Lattice Boltzmann model for liquid–vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. This model relies on a set of 25 off-lattice momentum vectors, whose Cartesian projections are the roots of the Hermite polynomial of order Q = 5 . The time evolution, spatial advection and gradient computations are performed using finite difference techniques. Our implementation is extensively benchmarked in the following contexts: the planar interface, the Laplace pressure test, the damping of shear and longitudinal waves, as well as the Galilean invariance test. We then investigate the liquid–vapour phase separation between two parallel walls kept at a constant temperature T w , which is smaller than the critical temperature T c , and discuss the main features of this process.