A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability.

*(English)*Zbl 0954.76076Summary: 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 |

##### Keywords:

lattice Boltzmann scheme; multiphase flow; nearly incompressible limit; distribution functions; interfacial dynamics; phase segregation; surface tension; molecular interactions; numerical stability; index function; two-dimensional Rayleigh-Taylor instability
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