The partial differential equation describing equilibrium radiation diffusion is strongly nonlinear, which has been widely utilized in various fields such as astrophysics and others. The equilibrium radiation diffusion equation usually appears over multiple complicated domains, and the material characteristics vary between each domain. The diffusion coefficient near the interface is discontinuous. In this paper, the equilibrium radiation diffusion equation with discontinuous diffusion coefficient will be solved numerically by the unsymmetric radial basis function collocation method. The energy term T4 is linearized by utilizing the Picard-Newton and Richtmyer linearization methods on the basis of the fully implicit scheme discretization. And the successive permutation iteration and direct linearization methods are applied to linearize the diffusion terms. The accuracy of the proposed methods is proved by numerical experiments for regular and irregular domains with different types of interfaces.

中文翻译：

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具有界面和不连续系数的非线性平衡辐射扩散方程的无网格方法


描述平衡辐射扩散的偏微分方程是强非线性的，已广泛应用于天体物理学等各个领域。平衡辐射扩散方程通常出现在多个复杂的域上，并且每个域之间的材料特性各不相同。界面附近的扩散系数是不连续的。在本文中，将采用非对称径向基函数搭配法对具有不连续扩散系数的平衡辐射扩散方程进行数值求解。能量项 T4 在完全隐式方案离散化的基础上，利用 Picard-Newton 和 Richtmyer 线性化方法进行线性化。并应用连续排列迭代和直接线性化方法对扩散项进行线性化。通过对具有不同类型界面的规则域和不规则域的数值实验证明了所提方法的准确性。