Localized radial basis function collocation method for long-time simulation of nonlinear transient heat conduction problems

This paper introduces a hybrid numerical method for simulating two- and three-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity over extended time intervals. The approach employs the Krylov deferred correction method for temporal discretization, which is particularly effective for dynamic simulations requiring high accuracy. After temporal discretization, the resulting nonlinear equation is solved in the spatial domain using the localized radial basis function collocation method, with its performance further improved by incorporating a newly developed radial basis function. Numerical experiments on two test cases validate the effectiveness and stability of the proposed hybrid method.