Multiple-distribution-function lattice Boltzmann method for one-dimensional Euler Equations

doi:10.1016/j.aml.2026.109942

Multiple-distribution-function lattice Boltzmann method for one-dimensional Euler Equations

2026-03-23

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DOI：10.1016/j.aml.2026.109942

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Compressible inviscid flows governed by the Euler equations are pivotal in aerospace engineering and astrophysics, yet their complex wave structures pose challenges to traditional numerical methods. This work proposes a novel multiple-distribution-function lattice Boltzmann method (MDF-LBM) for one-dimensional Euler equations. Inspired by the Lax–Wendroff scheme, the Euler equations are first reformulated into a cross-diffusion system, and a corresponding LBM framework is subsequently constructed. Direct Taylor expansion analysis demonstrates that the proposed model accurately recovers the macroscopic cross-diffusion system. Validation via the classic Sod shock tube problem shows excellent agreement with exact solutions across different grid resolutions. The model effectively captures shock waves, contact discontinuities, and rarefaction waves without spurious oscillations or artificial viscosity limiters, while retaining LBM’s intrinsic parallelism and simplicity.

Keywords:

Lattice Boltzmann method

Euler equations

compressible flow

shock capturing

multiple-distribution-function

Multiple-distribution-function lattice Boltzmann method for one-dimensional Euler Equations

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