中文摘要：

本文将自然单元法运用于二维半透明介质辐射与导热耦合问题的求解。自然单元法是基于自然邻近插值的无网格法,相对于其他无网格法,具有插值特性和支持域各向异性等特点。自然单元法采用自然邻近插值构造形函数,自然邻近插值包括Sibson插值和Laplace插值。本文介绍了Laplace插值的定义及其性质,对其收敛特性进行了研究。运用伽辽金加权余量法离散热辐射传递方程和能量方程,求解了方形区域和圆环区域辐射与导热耦合换热问题,通过与文献结果的对比验证了自然单元求解的有效性。

英文摘要：

Natural element method has been employed to solve two-dimensional coupled radiative and conductive heat transfer problems. Natural element method （NEM） is a kind of meshless method based on natural neighbor interpolation. Unlike most other meshless methods, the shape function used in NEM has interpolation property and its support domain is anisotropy. In the framework of NEM, the natural neighbor interpolations are employed to constructed shape function, such as Sibson interpolant and Laplace interpolant. Laplace interpolant is introduced in this paper, and the convergence property of it is investigated. The OMerkin weighted residual method is employed to discrete both the radiative heat transfer and energy equation. By using NEM, the coupled heat transfer problems in rectangular and cylindrical ring enclosures are solved. Correctness of the results is validated by comparison with those in the literature.