管道热边界层方程的迎风有限元分析

Upwind Finite Element Method on Temperature Boundary Layer in Pipeline

对于管道热边界层方程，除了采用动量积分方法求得理论解析解外，也可以用数值方法求解，如有限差分、有限体积、有限元等方法。理论解析解是采用一定的简化并忽略若干项之后得到的，因此，也只是一种近似解，数值解可以考虑完整的方程和各种边界条件，因而其解较为全面。采用伽辽金有限元方法求解，管道热边界层方程为标准的对流扩散方程，当对流项较强时，需要采用迎风方法，因而也给出了迎风有限元方法的模型。

Not only adapting theory analyses method may be used to solve analyzing solution for temperature boundary layer in Pipeline, but also may be adapted computational method, such as Finite Difference Method, Finite Volume Method, Finite Element Method, and son. Theory analyses solution is acquired that is simplified and neglected several terms of equation. So, it is only approximate solution. Computational solution may be considered a whole equation and the more various boundary conditions. Hence, the solution is more complete and all - round. The equation of temperature boundary layer in Pipeline is solved by applying Galerkin＇s finite element method in the paper. For the convection and diffusion equation, when the convection terms is stronger, the upwind method is required to adapt. So , upwind finite element model is given out, too, in the paper.