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.
Vignal, Philippe, Collier, Nathaniel O., Dalcin, Lisandro, Brown, D. L., & Calo, Victor M. (2016). An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering, 316(C). https://doi.org/10.1016/j.cma.2016.12.017
@article{osti_1394571,
author = {Vignal, Philippe and Collier, Nathaniel O. and Dalcin, Lisandro and Brown, D. L. and Calo, Victor M.},
title = {An energy-stable time-integrator for phase-field models},
annote = {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.},
doi = {10.1016/j.cma.2016.12.017},
url = {https://www.osti.gov/biblio/1394571},
journal = {Computer Methods in Applied Mechanics and Engineering},
issn = {ISSN 0045-7825},
number = {C},
volume = {316},
place = {United States},
publisher = {Elsevier},
year = {2016},
month = {12}}
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, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 316; ISSN 0045-7825