High resolution sharp computational methods for elliptic and parabolic problems in complex geometries

Frédéric Gibou, Chohong Min, Ron Fedkiw

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree node-based adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

Original languageEnglish
Pages (from-to)369-413
Number of pages45
JournalJournal of Scientific Computing
Volume54
Issue number2-3
DOIs
StatePublished - Feb 2013

Keywords

  • Diffusion
  • Elliptic
  • Ghost-fluid method
  • Level-set method
  • Octree
  • Parabolic
  • Poisson
  • Quadtree
  • Stefan

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