TY - JOUR
T1 - A General Strategy for Numerical Approximations of Non-Equilibrium Models – Part I: Thermodynamical Systems
AU - Zhao , Jia
AU - Yang , Xiaofeng
AU - Gong , Yuezheng
AU - Zhao , Xueping
AU - Yang , Xiaogang
AU - Li , Jun
AU - Wang , Qi
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 884
EP - 918
PY - 2018
DA - 2018/08
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12613.html
KW - Energy stable schemes, nonequilibrium models, thermodynamically consistent models, energy quadratization.
AB - <p style="text-align: justify;">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&#39;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.</p>