平面二维对流输移问题新解

在普适性好的三角形网格上，针对平面二维非恒定对流输移方程解，本文提出一个准三阶精度的数值方法。其 原理是沿着双特征线将二维对流经成特征关系，确定了任意时刻空间两点上待定解的解切关系，并利用三角面元顶点函数和导数值，解了作三角面元的中点约束，建立一个受限制的三次爱尔米特插值多项系，据此完成待求函数的数值解。

New method for computation of two-dimension advection transport

The computation of two-dimensional advection transport using current methods such as Alternating Direction Implicit Method and linear interpolation technique can be subject to numerical attenuation,parasite oscillation and poor reproduction of wave propagation when large time steps are used. The method described in this paper is based on two-dimensional method of characteristics. A characteristical numerical relation between n time-step and(n+1)time-step along the hi-characteristic lines has been found,so that the unknown value at n time-step can be calculated by using three-order Hermite polynomial which is established by using function and derivation in the triangle grid.The basic principles of the method as well as its application to four schematic test cases are described in detail.