Simulation of thermocapillary flow in a two dimensional cavity with lattice Boltzmann method

Thermocapillary flow driven by an unbalanced surface tension plays the most important role for mass and heat transport in floating zone melt crystal growth under microgravity. The authors develop both a serial and a parallel codes with lattice Bhatnagar-Gross-Krook(BGK) model using two distribution functions, and numerically study the thermocapillary flow in a two dimensional square cavity with a single free surface under microgravity condition. The serial code is developed by combining collision and propagation step, using a temporary array to continuously read distribution functions, and its performance is improved two times faster than the code with separating the collision and propagation step. The MPI parallel code is proposed utilizing one dimensional partitioning and non-blocking communication. The accurate and reliable results are achieved with both the serial and parallel codes by comparing with CFD results simulated by the finite volume method; the MPI parallel code has high performance.     

A new boundary treatment of lattice boltzmann method (LBM) for fully developed pressure-driven periodic incompressible fluid flow

This paper proposeds a new boundary treatment of Lattice Boltzmann Method (LBM) for fully developed pressure-driven periodic incompressible fluid flow. The pressure gradient, instead of equivalent body force, is applied to determine the particle distribution function on the periodic traverse sections for the fully developed pressure-driven periodic flow. Numerical simulations, including 2D pressure-driven poiseuille flow and fluid flow passing periodic square obstacles, are carried out using this new boundary treatment. Simulation results show that the proposed approach not only overcomes the nonphysical inlet and outlet flow disturbances (which the LBM simulation always suffers from using the existing pressure boundary methods), but also preserves the system periodicity and generates consistent pressure distribution with macroscopic periodic boundary conditions for the pressure-driven incompressible fluid flow.