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Nonlinear canonical Euler splitting meshfree method for strongly stiff radiation diffusion problem
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Q
刘
J
DOI：10.1016/j.enganabound.2026.106860.png)
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Abstract
En 中文
The strongly stiff radiation diffusion problems pose significant computational challenges due to their multi-scale temporal characteristics (such as radiation transport time scales and hydrodynamic time scales) and strong nonlinearity on complex geometric domain. The nonlinear canonical Euler splitting meshfree (NCESM) methods for 2D and 3D strongly stiff radiation diffusion problems are provided, which use the generalized explicit/implicit Euler method to solve the weakly stiff and strongly stiff subproblems. The nonlinear equations arising from the generalized implicit Euler method are solved by the simplified Newton method at each time level. Several numerical experiments on complex solution domains are presented by the comparison of the errors with the different RBFs, fully implicit simplified Newton iteration, direct linearization or IMEX methods. The results show the presented NCESM method based on Wendland’s C6 has the superiority of the accuracy. The iterative number in each simplified Newton iteration is about 2. The presented methods will be applied to solve other strongly stiff problems on irregular domains and developed higher-order time discretization methods in future.
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