Meshfree Methods based on RBFs and H-RBFs for 3-D 3-T Radiation Diffusion Equations in Irregular Domains

The high-dimensional radiation diffusion equations have a wide range of applications in inertial confinement fusion, magnetic confinement fusion, astrophysics, hypersonic, combustion and other fields. When the material itself is non-equilibrium, the diffusion equation model used to describe the process is a strongly nonlinear three temperature radiation diffusion equations. Moreover, when there are practical difficulties such as complex solution regions and distorted mesh deformation in high-dimensional radiation fluid motion, many methods are prone to computational distortion. Therefore, this paper proposes a meshfree method based on radial basis functions for solving the three-dimensional three temperature (3-D 3-T) radiation diffusion equations. The convergence analysis by the residual estimate based on the reproducing kernel functional space is provided. The new method overcomes the difficulties of irregular regions, strong nonlinearity, and strong coupling, and further improves the new method using hierarchical radial basis functions. The high accuracy and scalability of the proposed new methods were verified through specific numerical experiments.