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A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. (English) Zbl 0954.76076
Summary: We propose a lattice Boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit. The scheme simulates fluid flows by using distribution functions. The interfacial dynamics, such as phase segregation and surface tension, is modeled by incorporating molecular interactions. The lattice Boltzmann equations are derived from the continuous Boltzmann equation with appropriate approximations suitable for incompressible flow. We improve the numerical stability by reducing the effect of numerical errors in calculation of molecular interactions. An index function is used to track interfaces between different phases. Simulations of the two-dimensional Rayleigh-Taylor instability yield satisfactory results. The interface thickness is maintained at 3-4 grid spacings throughout simulations without artificial reconstruction steps.

MSC:
76M28 Particle methods and lattice-gas methods
76E17 Interfacial stability and instability in hydrodynamic stability
76T99 Multiphase and multicomponent flows
82D15 Statistical mechanics of liquids
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