Geodesic
Simulation of flows with vapor-liquid interfaces using lattice Boltzmann equation method
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 3, pp. 29-42

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The method of simulation of fluid flows with vapor-liquid interfaces including newly generated in bulk of liquid is proposed. Instead of discontinuity, interfaces between liquid and vapor are represented as thin transition layers of finite width (several nodes of lattice) where density changes smoothly from one bulk value to another (by analogy to shock-capturing method for shock waves in gasdynamics). In proposed variant of lattice Boltzmann equation (LBE) method, the phase transitions can be simulated for equations of state of arbitrary form. For flat transition layer, the coexistence curve is reproduced with high accuracy in the wide enough range of reduced temperature from the critical point down to $\tilde{T}\approx0.4$. For stationary vapor-liquid transition layers, the density relation was obtained of order $10^5$–$10^6$ that can not be realized using previous variants of LBE methods. 
@article{VNGU_2005_5_3_a2,
     author = {A. L. Kuperschtokh},
     title = {Simulation of flows with vapor-liquid interfaces using lattice {Boltzmann} equation method},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {29--42},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2005_5_3_a2/}
}
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A. L. Kuperschtokh. Simulation of flows with vapor-liquid interfaces using lattice Boltzmann equation method. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 3, pp. 29-42. http://geodesic.mathdoc.fr/item/VNGU_2005_5_3_a2/