Lattice Boltzmann model for non-ideal compressible fluid dynamics

S. A. Hosseini; M. Feinberg; I. V. Karlin

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arXiv · 2510.14712

Lattice Boltzmann model for non-ideal compressible fluid dynamics

S. A. Hosseini·M. Feinberg·I. V. Karlin

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Abstract

We present a new kinetic model and its lattice Boltzmann realization 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 regularization, 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.

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S. A. Hosseini, M. Feinberg, I. V. Karlin. 2025-10-16. Lattice Boltzmann model for non-ideal compressible fluid dynamics. https://arxiv.org/abs/2510.14712

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