非均质各向异性材料导热类问题的数值求解方法

A NUMERICAL METHOD FOR SOLVING HEAT CONDUCTION PROB-LEMS OF HITEROGENEOUS AND ANISOTROPEC MATERIALS

提出了一种求解非均质各向异性材料导热类问题的控制容积有限差分格式（ＣＶＦＤ）。这种格式以三角形为基本单元，以其对偶的Ｖｏｒｏｎｏｉ多边形为积分的控制容积，并假定控制容积内物性均匀，温度呈线性分布。该方法克服了控制容积有限元《ＣＶＦＥ）方法中同一个控制容积内温度梯度不一致的缺点。ＣＶＦＤ差分格式既能灵活适应复杂边界，又便于网格局部加密，同时还能满足局部守恒。当基本单元全为直角三角形时，该格式退化为结构网格的有限差分格式，便于移植到已有的计算软件中。

A control-volume finite-difference (CVFD) scheme for solving heat conduction problems of heterogeneous and anisotropic material is given. The control volumes are constructed around triangle venices and Voronoi polygon. It is-assumed that the properties of material are uniform, and the temperature varies linearly inside the control volumes, which overcomes the shortcomings of control-volume finite-element (CVFE) method abouy that the temperature gradients are not identical. CVFD method is suitable for complicated complicated and facilitate partial densification, and it can satisfy local equilibrium. When all the basic elements are right-angled triangles, this scheme degenerates to finite differential scheme used with structured grid. So it is easy to be transferred to presented computation software.