Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows

The aim of this paper is twofold: the first to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum transition regime; second present some new insights into thermo-hydrodynamic non-equilibrium (THNE) effects in phase separation process. Methodologically, DBM includes three main pillars: (i) determination fewest moment relations, which are required by description significant THNE beyond realm fluid mechanics, (ii) construction appropriate equilibrium distribution function recovering all desired moments, (iii) detection, description, presentation analysis moments ($f-f^{(eq)}$). incorporation additional higher-order thermodynamic considerably extends DBM's capability handling larger values liquid-vapor ratio, curbing spurious currents, ensuring mass-momentum-energy conservation. Compared with only first-order (Gan et al. Soft Matter 11,5336), model retrieves third-order super-Burnett level, accurate weak, moderate, strong cases even when local Knudsen number exceeds $1/3$. Physically, ending point linear relation between concerned physical parameter provides distinct criterion identify whether system near or far equilibrium. Besides, surface tension refrains around interface, but expands range strengthens intensity away interface through smoothing widening.