A General Strategy for Numerical Approximations of Non-Equilibrium Models – Part I: Thermodynamical Systems
Year: 2018
Author: Jia Zhao, Xiaofeng Yang, Yuezheng Gong, Xueping Zhao, Xiaogang Yang, Jun Li, Qi Wang
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 6 : pp. 884–918
Abstract
We present a general approach to deriving energy stable numerical approximations for thermodynamically consistent models for nonequilibrium phenomena. The central idea behind the systematic numerical approximation is the energy quadratization (EQ) strategy, where the system'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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12613
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 6 : pp. 884–918
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Energy stable schemes nonequilibrium models thermodynamically consistent models energy quadratization.