A general strategy for numerical approximations of non-equilibrium models–Part I: Thermodynamical systems

J. I.A. Zhao, Xiaofeng Yang, Yuezheng Gong, Xueping Zhao, Xiaogang Yang, J. U.N. Li, Q. I. Wang

Research output: Journal PublicationArticlepeer-review

48 Citations (Scopus)

Abstract

We present a general approach to deriving energy stable numerical approximations for thermodynamical consistent models for nonequilibrium phenomena. The central idea behind the systematic numerical approximation is the energy quadratization (EQ) strategy, where the sys-tem’s free energy is transformed into a quadratic form by introducing new intermediate variables. By applying the EQ strategy, one can develop linear, high order semi-discrete schemes in time that preserve the energy dissipation property of the original thermodynamically consistent model equations. The EQ method is developed for time discretization primarily. When coupled with an appropriate spatial discretization, a fully discrete, high order, linear scheme can be developed to warrant the energy dissipation property of the fully discrete scheme. A host of examples for phase field models are presented to illustrate the effectiveness of the general strategy.

Original languageEnglish
Pages (from-to)884-918
Number of pages35
JournalInternational Journal of Numerical Analysis and Modeling
Volume15
Issue number6
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Energy quadratization
  • Energy stable schemes
  • Nonequilibirum models
  • Thermodynamic consistent models

ASJC Scopus subject areas

  • Numerical Analysis

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