An energy-stable time-integrator for phase-field models

Vignal, Philippe; Collier, Nathaniel O.; Dalcin, Lisandro; Brown, D. L.; Calo, Victor M.

doi:10.1016/j.cma.2016.12.017

Title: An energy-stable time-integrator for phase-field models

Journal Article · Tue Dec 27 00:00:00 EST 2016 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2016.12.017· OSTI ID:1394571

^[1];

^[2];

^[3]; Brown, D. L. ^[4]; Calo, Victor M. ^[5]

King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Santa Fe (Argentina)
Univ. of Nottingham, Nottingham (United Kingdom)
Curtin Univ., Perth, WA (Australia); Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA (Australia)

Here, we introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1394571

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 316, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: An energy-stable time-integrator for phase-field models

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