近期，我院青年教师李猛的文章《Adaptive moving mesh methods for anisotropic surface diffusion and applications to solid-state dewetting》在国际期刊《Journal of Computational Physics》发表。

     摘要：In this work, we propose adaptive moving mesh methods for anisotropic surface diffusion and apply them to the numerical simulation of solid-state dewetting in thin films. The methods are formulated based on the mesh equidistribution principle, where a carefully crafted tangential velocity is used to dynamically redistribute the mesh points throughout the evolution. To accurately capture the evolving interface's geometric features, we design monitor functions that depend on the curvature kappa, its arc-length derivative kappa(2), and the squared curvature kappa(2), which guide adaptive node refinement and redistribution, enhancing mesh quality and numerical accuracy. For spatial discretization, the central finite differences are used, while the BDFk (k = 1, 2, 3, 4) methods are employed for temporal discretization. Furthermore, based on the established adaptive moving mesh methods, we develop several structure-preserving techniques using the Lagrange multiplier approach, ensuring that area conservation and energy stability are maintained throughout the simulation. Numerical experiments show that the proposed methods are highly compatible with anisotropic surface diffusion and solid-state dewetting, significantly improving mesh distribution and computational stability, while demonstrating exceptional adaptability and accuracy in simulating complex interface evolutions and efficiently capturing sharp corners and crystallographic features induced by anisotropic effects.

     论文链接：https://www.sciencedirect.com/science/article/pii/S0021999126007205?pes=vor&utm_source=clarivate&getft_integrator=clarivate