解常系数线性对流扩散方程的经典R-K法

A Classical R-K Method to Solve Linear Constant Coefficient Convection and Diffusion Equation

对流扩散方程是描述粘性流体运动的非线性方程的线性化模型方程,常系数线性对流扩散方程也常用差分法、有限体积法或有限元法来求解,但在处理实际问题时,这些方法往往因为解的精度不高而使计算结果不合理,而采用经典R-K法可以明显提高解的精确度.通过对实际计算结果的比较,该方法解的精度几乎与解析解的精度相同.

Convection and diffusion equation is the linear matrix equation of nonlinear equation describing glutinosity hydro- motion. Linear constant coefficient convection and diffusion equation are usually solved with the method of difference, finite cubage method and finite element method. But in solving practical problems, these methods, due to their low precision, can not come to reasonable results. The classical R - K method can significantly improve the precision. When compared with the practical calcu- lating results, this method is found almost of the same precision as that by performing analytic method.