Geodesic
Three-dimensional LBE simulations on hybrid GPU-clusters for the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels
Numerical methods and programming, Tome 13 (2012) no. 3, pp. 384-390.

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In the lattice Boltzmann equation method (LBE), the different phases of a substance are usually simulated as a one fluid. The algorithm of the LBE method is well suitable for parallelization on a large amount of stream processors that are included in modern Graphics Processing Units (GPU). Hybrid GPU-clusters allows us to exploit a new level of simulations of multi-physic problems. The 3D simulations of a spinodal decomposition were carried out on grids consisting of more than 250 million nodes. The 3D simulations of the anisotropic decay of binary mixtures of dielectric liquids with a solute gas under a strong electric field to a system of gas-vapor channels in a liquid that are parallel to the local electric field is performed. The gas-vapor channels expand because of the diffusion of a solute gas and due to a process of coalescence. The critical value of the uniform electric field decreases with an increase in the initial concentration of a solute gas. This indicates that such an electrostrictive mechanism of the generation, growth and branching of the channels during the breakdown of real dielectric liquids in the nanosecond range is possible.
Keywords: lattice Boltzmann equation method; phase transitions; dynamics of multiphase media; binary mixtures; breakdown of dielectric liquids; computer simulations; parallel computing; graphics processing units; hybrid supercomputers. 
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     author = {A. L. Kupershtokh},
     title = {Three-dimensional {LBE} simulations on hybrid {GPU-clusters} for the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels},
     journal = {Numerical methods and programming},
     pages = {384--390},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_3_a1/}
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A. L. Kupershtokh. Three-dimensional LBE simulations on hybrid GPU-clusters for the decay of a binary mixture of liquid dielectrics with a solute gas to a system of gas-vapor channels. Numerical methods and programming, Tome 13 (2012) no. 3, pp. 384-390. http://geodesic.mathdoc.fr/item/VMP_2012_13_3_a1/