二维稳态热传导问题的正六边形流形元研究

2D Steady Heat Conduction Analysis With the Regular Hexagon Numerical Manifold Method

发展了用于分析二维稳态热传导问题的多边形数值流形方法(numerical manifold method,NMM).根据热传导问题的控制方程、边界条件以及多边形NMM的温度近似函数,采用修正变分原理导出了多边形NMM求解稳态热传导问题的总体方程,给出了多边形单元上的域积分策略.考虑到NMM中数学覆盖系统可不与物理域边界一致以及规则单元的精度优势,采用Wachspress正六边形数学单元对两个典型热传导问题进行了仿真,计算结果与参考解能较好地吻合,表明多边形NMM可以很好地模拟平面稳态热传导问题.

The polygonal numerical manifold method （NMM） was developed to analyze two-di- mensional （2D） steady heat conduction problems. Based on the governing equation, the bound- ary conditions and the NMM temperature approximation, the discrete NMM equations were de- duced according to the modified variational principle. The domain integration schemes on the polygonal elements were presented. Due to the independence between the mathematical cover system and the physical domain and in virtue of the accuracy advantage of regular polygonal el- ements, the Wachspress regular hexagon mathematical elements were adopted in 2 typical ex- amples, and the computed temperatures agreed well with the referential ones. The study shows that the regular hexagon NMM can well tackle 2D heat conduction problems.