中文摘要：

对一类非线性多孔介质方程构造了格子Boltzmann求解模型。由LBGK模型出发,通过合理补充演化方程中的源项分布函数以及适当选取局部平衡态分布函数,恢复出宏观的非线性多孔介质方程。几个典型多孔介质方程的数值模拟验证了模型精度和有效性。

英文摘要：

A lattice Boltzmann model for the nonlinear porous media equation is established to recover the macro nonlinear porous media equation by adding the distribution functionof the source term and selecting the local equilibrium distribution function in evolution equation.Simulation for some typical porous media equations verifies the precision and feasibility of the model.