二维分层流的格子Boltzmann数值模拟

基于格子Boltzmann方法，采用改进的自由能模型，对二维分层流和“气泡”迁移现象进行了数值模拟。计算模型中，边界条件处理采用了法向反弹假定，这种处理方法具有二阶精度且简单易行。在给定的条件下，对分层流进行了数值模拟，流速的计算值与其理论解非常吻合，最大相对误差不超过0.3％。常规自由能模型不能满足伽利略不变性，在模拟气泡运动时，圆形气泡往往会变为椭圆形；而改进的自由能模型满足伽利略不变性，在模拟气泡时其形状不会失真。最后，给出了一个“气泡”迁移的数值仿真，在计算了200 000个时间步后，气泡仍然保持原来的形状。数值试验的结果验证了模型的有效性与可靠性。

Lattice Boltzmann simulation of two_dimensional stratified flow

Based on the lattice Boltzmann(LB) method,the improved LB model using free-energy approach is proposed and is used to simulate the two-dimensional stratified flow and "bubble" movement.The normal rebouding assumption is used in the model,which has the second order precision and is relatively easy to be implemented in the calculation.With the given conditions,the stratified flow is modeled and the calculated flow field is very consistent to the analytical solution.The maximum relative error of the flow speed is less than 0.3%.The conventional free-energy models are not Galilean invariant and the circular bubble will always become elliptical.The improved free-energy model is Galilean invariant,the shape of the moving "bubble" will not be anamorphic.In the given example of moving "bubble",the bubble is still the original shape after 200 000 time steps.The effectiveness and reliability of the model are demonstrated by numerical examples.