Long time numerical simulations for phase-field problems using p-adaptive spectral deferred correction methods

Xinlong Feng, Tao TANG, Jiang Yang

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

A high-order and energy stable scheme is developed to simulate phase-field models by combining the semi-implicit spectral deferred correction (SDC) method and the energy stable convex splitting technique. The convex splitting scheme we use here is a linear unconditionally stable method but is only of first-order accuracy, so the SDC method can be used to iteratively improve the rate of convergence. However, it is found that the accuracy improvement may affect the overall energy stability which is intrinsic to the phase-field models. To compromise the accuracy and stability, a local p-adaptive strategy is proposed to enhance the accuracy by sacrificing some local energy stability in an acceptable level. The proposed strategy is found very useful for producing accurate numerical solutions at small time (dynamics) as well as long time (steady state) with reasonably large time stepsizes. Numerical experiments are carried out to demonstrate the high effectiveness of the proposed numerical strategy.

Original languageEnglish
Pages (from-to)A271-A294
JournalSIAM Journal of Scientific Computing
Volume37
Issue number1
DOIs
Publication statusPublished - 2015

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Adaptive scheme
  • Energy stable convex splitting
  • Long time simulation
  • Phase-field models
  • Semi-implicit spectral deferred correction methods

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