Density gradient model in spherically symmetric formulation and its explicit-implicit dissipative discretization for the study of phase boundary dynamics

An unconditionally gradient-stable (dissipative) numerical method is developed for solving a conservative model of the density gradient in the spherically symmetric formulation. The algorithm is constructed using Eyre’s method based on a convex splitting of the free energy of the system. The gradient stability of the constructed algorithm in the semidiscrete and fully discrete cases is proved. The theoretical results are confirmed by test computations. The proposed numerical method is used to analyze the influence exerted by the way of specifying the diffusion mobility on the evolution of the phase boundary.