中文摘要：

将一种新的格子玻尔兹曼模型（简称LB模型）应用于土壤水流下渗过程的探讨.在恰当的时间和空间多尺度化方案基础上,给出了Richards下渗方程的LB模型所对应的宏观量和平衡态分布函数形式.通过对扩散方程和线性Richards方程的分析,LB模型的模拟结果与分析解相吻合,并详细探讨了弛豫系数、网格步长和时间步长等参数对计算误差的影响.与Philips解的比较表明,该LB模型可成功应用于非线性Richards下渗方程的求解,并在计算稳定性和处理非线性等方面展现出很好的优点.

英文摘要：

A new kind of the lattice Boltzmann model （LB model） was applied to the simulation of vertical infiltration process in unsaturated soils.Based on suitable multi-scale algorithms for time and space,the macroscopic quantity and the equilibrium distribution functions corresponding to the LB model for the Richards equation were proposed.The linear diffusion equation and the linear Richards equation were discussed.The simulated results of the LB model agreed with the analytical solutions.The influences of some parameters such as relaxation time coefficient,lattice size and time step on the computing error were analyzed.A comparison with the classical Philip＇s solutions shows that the proposed LB model can be employed to successfully solve the nonlinear Richards equation,and it achieves good merits in computing stability and nonlinearity treatment and so on.