对流扩散方程局部分析解的数值模拟

本文提出了数值求解对流扩散方程的局部解析算法。首先将方程在一个时间步内线性化，然后，将解表示为初始各单元脉冲解的迭加，如此得到的近似解是由初始单元解表达的解析式，具有与一般数值方法(差分、有限元等)完全不同的优势。分别对一维和二维方程的几个典型算例进行了计算，获得了令人满意的数值结果，精度高且没有稳定性的限制，说明本方法具有较强的应用价值。

The numerical simulation of advection-diffusion equation by local analytical method

A numerical method based on the local linear analytical solution is given for the nonlinear advection diffusion equations. The original nonlinear equation is linearized using the value at the previous time step. The solution at the next time step can be expressed as the summation of the exact solutions obtained from the local impulse. Extensive numerical experimetns show that the new numerical method in this paper has particular advantages, for example, high accuracy, no stability problem.