A level set approach for diffusion and Stefan-type problems with Robin boundary conditions on quadtree/octree adaptive Cartesian grids

作者：Papac Joseph^*; Helgadottir Asdis; Ratsch Christian; Gibou Frederic

来源：Journal of Computational Physics, 2013, 233: 241-261.

DOI：10.1016/j.jcp.2012.08.038

• Level set method
• Epitaxial growth
• Diffusion
• Stefan problem
• Sharp interface
• Robin boundary condition

We present a numerical method for simulating diffusion dominated phenomena on irregular domains and free moving boundaries with Robin boundary conditions on quadtree/octree adaptive meshes. In particular, we use a hybrid finite-difference and finite-volume framework that combines the level-set finite difference discretization of Min and Gibou (2007) [13] with the treatment of Robin boundary conditions of Papac et al. (2010) [19] on uniform grids. We present numerical results in two and three spatial dimensions on the diffusion equation and on a Stefan-type problem. In addition, we present an application of this method to the case of the simulation of the Ehrlich-Schwoebel barrier in the context of epitaxial growth. Published by Elsevier Inc.

• 出版日期2013-1-15