Lattice Boltzmann model for non-ideal compressible fluid dynamics

We present a new kinetic model and its lattice Boltzmann realisation for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via quasi-equilibrium attractors, ensuring positive-definite and Galilean-invariant Navier–Stokes dissipation rates. This construction circumvents the need for extended stencils or ad hoc regularisation, while maintaining numerical stability and thermodynamic consistency across a broad range of flow regimes. The resulting model accurately reproduces both the Euler and Navier–Stokes hydrodynamic limits. As a stringent validation, we demonstrate, for the first time within a lattice Boltzmann framework, quantitatively accurate simulations of shock–drop interactions at Mach numbers up to 1.47. The proposed approach thus extends the applicability of lattice Boltzmann methods to high-speed, non-ideal compressible flows with a minimal kinetic stencil.