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An inventory of Lattice Boltzmann models of multiphase flows
, 2008
"... This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by ChapmanEnskog techniques the corresponding macroscopic equations. The singular interface (YoungLaplaceGauss) model is described briefly, with a discussion of its limi ..."
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This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by ChapmanEnskog techniques the corresponding macroscopic equations. The singular interface (YoungLaplaceGauss) model is described briefly, with a discussion of its limitations. The diffuse interface theory is discussed in more detail, and shown to lead to the singular interface model in the proper asymptotic limit. The Lattice Boltzmann method is presented in its simplest form appropriate for an ideal gas. Four different Lattice Boltzmann models for nonideal (multiphase) isothermal flows are then presented in detail, and the resulting macroscopic equations derived. Partly in contradiction with the published literature, it is found that only one of the models gives physically fully acceptable equations. The form of the equation of state for a multiphase system in the density interval above the coexistance line determines surface tension and interface thickness in the diffuse interface theory. The use of this relation for optimizing a numerical model is discussed. The extension of Lattice Boltzmann methods to the nonisothermal situation is discussed.
Maximum Entropy Boundaries in Lattice Boltzmann Method
"... Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend on dimensionality, LBM scheme, boundary geometry; which is numerically stable, accurat ..."
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Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend on dimensionality, LBM scheme, boundary geometry; which is numerically stable, accurate and local and has a good physical background. This technique, called a maximum entropy method, utilizes the idea of recovering unknown populations on boundary nodes through minimizing node state deviation from equilibrium while assuring velocity or temperature restrictions. Also, theoretical justifications of a popular ZouHe boundaries technique and isothermal boundaries algorithm are provided on the basis of the method derived. Finally, while conducting numerical benchmarks, typical straight boundaries algorithm (ZouHe) was
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, 2009
"... The importance of smallscale dynamics on largescale magmatic processes. by ..."
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The importance of smallscale dynamics on largescale magmatic processes. by