【摘要】 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问题化成特征关系，确定了任意时刻空间两点上待定解的确切关系，并利用三角面元顶点函数和导数值，解除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．在概化的平面区域内，采用上述方法模拟了二维初始浓度高斯分布和水流激波在旋转速度场及均匀速度场上的对流输移问题，结果表明方法在优化幅值衰减和数值扰动以及计算效率方面具有相当的发展潜力和应用前景．更多还原

【Abstract】 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.更多还原