热传导问题的非协调数值流形方法

数值流形方法通过引入数学与物理双重网格，将插值域与积分域分别定义在两个不同的覆盖上，其优点是网格划分随意，不受复杂边界形状和材料界面的限制，是较之于有限元方法更一般化的数值模拟方法。在计算精度方面，数值流形方法远远高于有限元法。但它的精度还是不够理想。为此本文在单元总体位移场上附加非协调位移基本项，使单元位移函数趋于完全，构造了非协调流形单元来改善流形单元的计算精度和计算效率，并将其应用于热传导问题，推导了势问题的非协调数值流形方法。

Incompatible Numerical Manifold Method Based on Heat Exchange Problem

Based on the double meshes of mathematics and physics in numerical manifold method, domains of interpolation and integration were defined on two different covers respectively. The merit of this method is arbitrary mesh discretization, and no constraints of complex geometrical shape and material interface, and the method is more general compared wirh conventional finite element method. But its computing accuracy is no perfect, so the incompatible displacement term is added in total element displacement function, it makes the displacement function tend to entire, and establishes an incompatible manifold element to improve computing efficiency. The method is applied to heat exchange problem, and the incompatible numerical manifold method based on potential problem was presented.