Abstract
An extended Boltzmann equation is constructed to model phase transitions with anisotropic effects. It is directly transformed into a discrete kinetic scheme in both time and phase space. The new scheme can be used to derive anisotropic lattice Boltzmann-phase field equation and convective diffusion equations. A lattice Boltzmann algorithm with the anisotropic streaming-relaxation operator is proposed, and numerical simulations of liquid–solid phase transition are performed as examples. The results agree well with previous numerical data and analytical solutions. It demonstrates that the scheme has acceptable numerical accuracy and computational efficiency, and the scheme can be used to study anisotropic liquid–solid phase transitions. This work provides an alternative numerical approach to model and simulate phase transitions with relatively fast computational efficiency.
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