Abstract
We investigate a kinetic model for compressible non-ideal fluids. The model imposes the local thermodynamic pressure through a rescaling of the particle’s velocities, which accounts for both long- and short-range effects and hence full thermodynamic consistency. The model is fully Galilean invariant and treats mass, momentum, and energy as local conservation laws. The analysis and derivation of the hydrodynamic limit is followed by the assessment of accuracy and robustness through benchmark simulations ranging from the Joule–Thompson effect to a phase-change and high-speed flows. In particular, we show the direct simulation of the inversion line of a van der Waals gas followed by simulations of phase-change such as the one-dimensional evaporation of a saturated liquid, nucleate, and film boiling and eventually, we investigate the stability of a perturbed strong shock front in two different fluid mediums. In all of the cases, we find excellent agreement with the corresponding theoretical analysis and experimental correlations. We show that our model can operate in the entire phase diagram, including super- as well as sub-critical regimes and inherently captures phase-change phenomena.
Highlights
The lattice Boltzmann method (LBM) is a kinetic-theory approach to the simulation of hydrodynamic phenomena with applications ranging from turbulence [1,2] to microflows [3,4] and multiphase flows [5,6,7,8]
While LBM has proven successful in a wide range of fluid mechanics problems [9,10], it is well known that the fixed velocity set restricts conventional LB models to low-speed incompressible flows [9]
We study the behavior of a perturbed shock-front in both an ideal gas as well as a van der Waals (vdW) fluid at Mach number Ma = 3
Summary
The lattice Boltzmann method (LBM) is a kinetic-theory approach to the simulation of hydrodynamic phenomena with applications ranging from turbulence [1,2] to microflows [3,4] and multiphase flows [5,6,7,8]. While LBM has proven successful in a wide range of fluid mechanics problems [9,10], it is well known that the fixed velocity set restricts conventional LB models to low-speed incompressible flows [9]. This promoted significant research efforts, which were directed towards the development of compressible LB models [11,12,13,14,15], but they are typically limited to ideal gas. This includes phenomena such as rarefaction shock waves [16,17,18,19], acoustic emission instability [20,21], inversion line (change of sign of the Joule–Thomson coefficient), phase transition, surface tension, and super-critical flows
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