报告人：许传炬教授

报告题目：Numerical solutions of the phase-field modeling of interfacial dynamics.

报告摘要：

(1) The interfacial dynamics of immiscible and incompressible two-phase fluids is of great interest but computationally not easy to resolve. In this talk, we will focus on a phase field description of the interfacial dynamics. The model is a set of coupling equations, which consists of the Navier-Stokes equations and the Cahn-Hilliard equation. The talk starts with a review of the existing methods for numerical solutions of the Navier-Stokes-Cahn-Hilliard coupling equations. Then we propose and analyze a class of efficient time-stepping schemes for the model. A detailed comparison with existing schemes will be presented, and the advantage of the new schemes are highlighted.

(2) Also, we propose and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes are based on an auxiliary variable approach for the Allen-Cahn equation and delicate treatment of the terms coupling the Allen-Cahn equation and temperature equation. The idea of the former is to introduce suitable auxiliary variables to facilitate construction of high order stable schemes for a large class of gradient flows. We propose a new technique to treat the coupling terms involved in the crystal growth model and introduce suitable stabilization terms to result in totally decoupled schemes, which satisfy a discrete energy law without affecting the convergence order.

报告时间：2022年5月28日09:00-12:00

报告形式：腾讯会议；会议号：812-505-935

报告人简介：许传炬，厦门大学数学科学学院特聘教授，博士生导师。1986年厦门大学本科，1989年巴黎南大学硕士，1993年巴黎第六大学博士。主要研究领域：计算流体谱元法，相场模型及其算法，分数阶偏微分/积分方程理论和数值计算。