中文摘要：

求解大Pelect（Pe）数的对流扩散方程是一个困难的问题。刚度矩阵刚性比过大以及难满足自伴随性,使得结果有假扩散或严重的越界现象。本文通过引入迎风格式和变分多尺度方法改善刚度矩阵,基于经典的算例旋转场问题验证了格式的可靠性。

英文摘要：

It is a difficult to solve convection-diffusion equations with large Pelect number（Pc）. The stiff ratio is too large for the stiff matrix to be self-adjoint, which causes streamwise false diffusion or serious overshoots and undershoots in numerical results. In this paper, we introduce an upwind scheme and a variational multiscale method to improve the stiff matrix, and validate the reliability through the classical rotation field problem.