Adaptive Mesh Refinement Computation of Solidification Microstructures Using Dynamic Data Structures

Nikolas Provatas, Nigel Goldenfeld, Jonathan Dantzig

Research output: Contribution to journalArticlepeer-review


We study the evolution of solidification micro structures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the phase-field model at low undercooling. In particular, we show that the computational complexity of solving any phase-boundary problem scales with the interface arclength when using an adapting mesh. Moreover, the use of dynamic data structures allows us to simulate system sizes corresponding to experimental conditions, which would otherwise require lattices greater than 217 × 217 elements. We examine the convergence properties of our algorithm. We also present two-dimensional, time-dependent calculations of dendritic evolution, with and without surface tension anisotropy. We benchmark our results for dendritic growth with microscopic solvability theory, finding them to be in good agreement with theory for high undercoolings. At low undercooling, however, we obtain higher values of velocity than solvability theory at low undercooling, where transients dominate, in accord with a heuristic criterion which we derive.

Original languageEnglish (US)
Pages (from-to)265-290
Number of pages26
JournalJournal of Computational Physics
Issue number1
StatePublished - Jan 1 1999

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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