@Article{CiCP-33-477,
author = {Wang , Weiwen and Xu , Chuanju},
title = {A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {2},
pages = {477--510},
abstract = {<p style="text-align: justify;">Thermal phase change problems are widespread in mathematics, nature,
and science. They are particularly useful in simulating the phenomena of melting
and solidification in materials science. In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase
change model, which is the coupling of a heat transfer equation and a phase field equation. The unconditional energy stability and consistency error estimates are rigorously
proved for the proposed schemes. A detailed implementation demonstrates that the
proposed method requires only the solution of a system of linear elliptic equations at
each time step, with an efficient scheme of sufficient accuracy to calculate the solution
at the first step. It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps. Adaptive time step
size strategies can be applied to further benefit from this unconditional stability. Numerical experiments are presented to verify the theoretical claims and to illustrate the
accuracy and effectiveness of our method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0183},
url = {http://global-sci.org/intro/article_detail/cicp/21497.html}
}