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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。
In this paper, the natural element method is applied to solve the two-dimensional translucent medium radiation and thermal conductivity coupling problem. The natural element method is based on the meshless method of natural neighbor interpolation. Compared with other meshless methods, the natural element method has the characteristics of interpolation and anisotropy of supportive fields. Natural element method uses natural neighbor interpolation to construct shape function. Natural neighbor interpolation includes Sibson interpolation and Laplace interpolation. This paper introduces the definition and properties of Laplace interpolation, and studies its convergence properties. By using the Galerkin weighted residual method, the heat transfer equation and the energy equation are solved. The heat transfer between the radiation and the heat transfer in the square and annular regions is solved. The comparison of the results with the literature results verifies the validity of the natural element solution.