报告地点：行健楼学术活动室526

邀请人：南彩霞博士

摘要：Thermal phase change phenomena, including dendritic solidification and alloy phase transformations, present significant challenges for accurate numerical simulation. In this paper, we focus on the heat and Allen–Cahn coupled equation modeling the thermal phase change, and propose a high-order original energy-preserving Additional Parametric Functions Integrating Factor Runge-Kutta method (APF-IFRK) for the coupling model. The main contributions and novelties of our method are summarized as follows: (i) An energy-consistent reformulation is developed by incorporating the original energy dissipation law into the coupled system. (ii) A relaxed regularity requirement is achieved as the method operates without artificial stabilization. Our approach avoids the need to estimate the Lipschitz constant, requiring only that the nonlinear term be locally Lipschitz continuous in a strip along the exact solution. Rigorous analysis demonstrates that the APF-IFRK framework maintains energy stability while inheriting the high-order accuracy of classical IFRK schemes. Numerical experiments on the coupled thermal phase change systems confirm superior structure-preservation properties compared to IFRK approaches. The proposed methodology establishes a general paradigm for developing energy-stable, high-order time discretization schemes applicable to broad classes of gradient flow systems.

报告人简介：宋怀玲，湖南大学数学学院教授，博士生导师，从事数学理论、计算方法和高效数值算法的教学和科研工作。本科与博士均毕业于山东大学，主要研究兴趣包括相场模型、相场耦合模型、非局部模型和多孔介质两相流问题的高阶数值方法的建立以及模型约化与应用等。相关研究成果发表在Computer Methods in Applied Mechanics and Engineering、Journal of Computational Physics、Journal of Scientific computing、Communications in Computational Physics等计算数学国际期刊，主持了包括国家自然科学基金，天元数学交流项目，湖南省面上项目等多项项目。