Geodesic
Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method
Numerical methods and programming, Tome 15 (2014) no. 2, pp. 317-328.

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A new method is proposed for the computation of heat and mass transfer for the modeling of flow of a medium with liquid-vapor phase transitions using the lattice Boltzmann equations (LBE). When the phase boundaries are present, it is necessary to consider the equation of energy transfer. A second set of LBE distribution functions is introduced in the form of a passive scalar that describes the transfer of internal energy. In order to eliminate the spurious diffusion of energy at the interface with a high density ratio, special pseudo-forces are introduced to prevent the passive scalar from expansion. The thermal conductivity and the pressure work are taken into account in the energy equation. The latent heat of evaporation and condensation is accounted in the energy equation for the inner region of a thin liquid-vapor transition layer. This allows one to avoid tracking the interfaces. Several simple tests were carried out to demonstrate all the aspects of the processes considered. It is shown that the Galilean invariance and the scaling of thermal conduction processes hold. The proposed method has a low scheme diffusion for the internal energy and can be applied for modeling a wide range of flows of two-phase media with the mass and heat transfer.
Keywords: lattice Boltzmann method, dynamics of multiphase fluids, heat and mass transfer, mesoscopic methods, computer simulations.
Mots-clés : phase transitions 
@article{VMP_2014_15_2_a10,
     author = {A. L. Kupershtokh and D. A. Medvedev and I. I. Gribanov},
     title = {Modeling of thermal flows in a medium with phase transitions using the lattice {Boltzmann} method},
     journal = {Numerical methods and programming},
     pages = {317--328},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a10/}
}
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A. L. Kupershtokh; D. A. Medvedev; I. I. Gribanov. Modeling of thermal flows in a medium with phase transitions using the lattice Boltzmann method. Numerical methods and programming, Tome 15 (2014) no. 2, pp. 317-328. http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a10/