In the past three decades, the Lattice Boltzmann (LB) method has emerged as a conceptually different approach of CFD. The first computationally viable realization dates back to the late 80s. The LB scheme governs fluid motions at a mesoscopic level that is intermediate between the microscopic and the macroscopic. Capturing the kinetic behavior of collections of particles distributed on a lattice is here preferred to solving non-linear PDEs. This seems crazy, however, most details at the mesoscopic level play actually no role at the macroscopic level. Therefore, much simpler kinetic equations may be designed retaining only the physical features that pertain at the macroscopic level. This is, in short, the rationale behind the LB approach.

Recently, such kinetic modeling has proved itself to be physically relevant to simulate the dynamics of superfluid Helium (He-II) compliant to the two-fluid model developed by Tisza & Landau (1941). Systematic simulations of thermal counterflows of He-II in a channel have shed some new light on the long debated thresholds of instabilities observed experimentally.