High-order modeling of multiphase flows: Based on discrete Boltzmann method

The high-order kinetic model for compressible multiphase flow is presented within the framework of the discrete Boltzmann method (DBM). Based on the Carnahan-Starling state equation, this model can describe the phase transition by introducing a source term of molecular interaction on the right-hand side of the Boltzmann equation. Meanwhile, the force term is incorporated to describe the external force. Through Hermite polynomial expansion, the equilibrium distribution function is expressed. Compared to the Navier- Stokes equations, the DBM provides more detailed and accurate information on both hydrodynamic and thermodynamic non-equilibrium effects. Finally, the model is verified through several typical benchmarks, including the liquid-vapor coexistence curve, free-falling process, shock wave, sound wave, thermal phase separation, and two-bubble oblique collision.