RESUMEN
It has recently been shown that altering the shape of the metastable and unstable branches of an equation of state (EOS) can substantially improve the numerical accuracy of liquid and vapor densities in the pseudopotential lattice Boltzmann method [Peng et al., Phys. Rev. E 101, 063309 (2020)2470-004510.1103/PhysRevE.101.063309]. We found that this approach reduces stability of the method in nonequilibrium conditions and is unstable for bubbles at low reduced temperatures. Here we present an improved method for altering the shape of the metastable and unstable branches of the EOS which remains stable for both equilibrium and nonequilibrium situations and has no issues with bubbles. We also performed a detailed study of the stability of the methods for a droplet impact on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remained stable for a density ratio of up to 3.38×10^{4}.
RESUMEN
One attractive feature of the original pseudopotential method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function. In order to improve the method, regarding thermodynamic consistency and control of surface tension, different approaches were developed in the literature, such as multirange interactions potential and modified forcing schemes. In this work, a strategy to combine these enhancements with an appropriate interaction force field using only nearest-neighbor interactions is devised, starting from the desired pressure tensor. The final step of our procedure is implementing this external force by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Static tests showed that current procedure is suitable to control the surface tension and phase densities. Based on thermodynamic principles, it is devised a solution for phase densities in a droplet, which states explicitly dependence on the surface tension and interface curvature. A comparison with numerical results suggest a physical inconsistency in the pseudopotential method. This fact is not commonly discussed in the literature, since most of studies are limited to the Maxwell equal area rule. However, this inconsistency is shown to be dependent on the equation of state (EOS), and its effects can be mitigated by an appropriate choice of Carnahan-Starling EOS parameters. Also, a droplet oscillation test was performed, and the most divergent solution under certain flow conditions deviated 7.5% from the expected analytical result. At the end, a droplet impact test against a solid wall was performed to verify the method stability, and it was possible to reach stable simulation results with density ratio of almost 2400 and Reynolds number of Re=373. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behavior.