中文摘要：

将格子玻尔兹曼方法应用于非线性热传导方程的求解，详细推导一种新的LatticeBoltzmann模型，并给出新方法所对应的多尺度方案和宏观量形式．导热系数与温度之间满足多项式函数关系，计算中模拟了不同的参数情况，并与线性热传导方程的理论解进行比较．新的LatticeBohzmann方法展现出极大的灵活性和普适性，具有很好的应用前景．

英文摘要：

Lattice Boltzmann method is employed to study nonlinear heat conduction problems. A kind of lattice Boltzmann model is derived in details and multi-scale algorithm and macroscopic quantity are selected. It is proposed to solve transient responses of nonlinear heat conduction problems. The relation between heat conductivity and temperature meets the multi-polynomial function. Different parameters are considered to verify feasibility of the proposed method. Simulation results are illustrated with comparison in linear case.