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

  • Authors:

  • Joseph Papac;Asdis Helgadottir;Christian Ratsch;Frederic Gibou

  • Affiliations:

  • Mathematics Department, University of California, Los Angeles, CA 91405, United States;Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States;Mathematics Department, University of California, Los Angeles, CA 91405, United States;Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States and Computer Science Department, University of California, Santa Barbara, CA 93106, United State ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

Quantified Score

Hi-index 31.45

Visualization

Abstract

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.